As I understand it, crosses are burdens that we haven't caused or sought, but just the result of life and the things that happen.  And that we are to accept these crosses without complaint understanding that we can offer them up and use them for our sanctification.

Now on the other hand, consequences are the result of our choices, actions and ultimately sins, things that happen when we go outside of God's will for our lives.

I had a surgical sterilization two decades ago after our second child was born.  A couple of pertinent factors: I wasn't raised Catholic, had no Catechism of any kind and was "agnostic" until AFTER this surgery had been performed.  I found out 4 years after the surgery that I'd committed a grave sin in the eyes of God and I've been suffering with the pain and regret of this transgression ever since.

The thing is that my H and I had/have always contracepted except for two tiny windows of time when we intentionally sought to conceive.  Our relationship has always been impacted by this fact and I have never ever felt a sure trust and respect from my H about the "act" as having any meaning except as a physically pleasurable thing to do.

Specifically, what I understand now more than ever, although I did have some sense of pain and unhappiness about feeling like an object for our entire relationship, is that the conjugal act exists for two reasons:

 1) procreation and 2) preventing one or both spouses from committing adultery.

I have never felt any bond with my H because of the conjugal act.  How could I? The Church Fathers have said time and again that the act of contraception puts a real physical and emotional and spiritual barrier between the spouses.

So I don't think the constant pain and distance I've felt all these years is a cross, I think it's a consequence of the sin I've committed and my question comes now to penance.  As soon as I understood what I'd done, I went to Confession, although I wasn't a Catholic at that time. My H confessed as well, but he thought and still seems to think that once you've confessed and been forgiven, that's all you have to do and you can live your life.  He thinks that it's a lack of belief in God not to trust in His mercy and forgiveness. But I know we still, I still have to pay for this crime against God.

I do do penance in general.  I have asked my priest about the conjugal act in regard to the grave sin committed and he said I'd better maintain that act evfen thought that sin was committed.  But my conscience* will not rest.  In my heart of hearts I believe that the punishment that fits the crime is probably to not live as husband and wife anymore. But my H will not agree to that. And I can't do this unilaterally and I am afraid of what it would do to our marriage because honestly without really strong spiritual reasons, it would kill our marriage, considering the condition it's been in for the last 5-6 years.  

*But I don't know if demons are manipulating my emotions about this.  I was listening to Fr. Ripperger yesterday, a talk called "Spiritual Protection" and he said that the demons will use your past sins against you and call up your emotions and encourage despair. I see that happening to me. I have been dogged by thoughts frequently, more frequently than ever the last few years, and thinking very negatively about my H in particular.  I could see that the demons would like to use this against our marriage and cause division and strife.

Also, I did spend quite a bit of time after learning about the grave matter of this sin, trying to find out about having reversal surgery.  It was very expensive, dangerous because of it being surgery and being put under anesthesia, not guaranteed and increased the chances of an ectopic pregnancy (which would mean the baby would attach to the fallopian tube instead of the uterine wall, and would have to be "removed" i.e., aborted, or we both would die) AND I had two babies at that time and couldn't see further risking my life and not being there to raise them.

I found out that there is no official teaching on paying penance for this sin.  Some people of the NFP variety advocated only having relations on fertile days.  A theologian made the point that this is the only sin where one confesses it and goes back to doing the thing that was wrong in the first place. Not unlike the divorced and remarried situation. But the Church does not require surgery and also does not ask that the married couple abstain for the rest of their lives.

That said, we all know that there seems to be no way to really pay for this except abstinence.

This is tearing me apart, happy demons all, and I know I have to come to some resolution, but maybe that is a false goal.  Maybe this continual unhappiness and torment IS the penance I am to uncomplainingly pay and maybe if I can master never expressing it or trying to make my H understand, it can be meritorious.  

It's the hardest thing of all to engage in the marital act unfeelingly and unhappily and yet having to pretend otherwise.

crosses are burdens that we haven't caused or sought,

We do indeed cause them and seek them when we are disobedient.  
They're an act of love, to redeem our sinful lives and sometimes to reward the holy.

Praise God that you have a well developed sensus Catholicus and a humble heart.

As soon as I understood what I'd done, I went to Confession, although I wasn't a Catholic at that time.

I presume you confessed this specifically since your conversion?

In a way, you're sort of like Dorothy in the Wizard of Oz.  She had the answer all along, but didn't realize it.  You identified the remedies in the quotes from the authorities in your life:

I have asked my priest about the conjugal act in regard to the grave sin committed and he said I'd better maintain that act

 <Fr. Rippinger> said that the demons will use your past sins against you and call up your emotions and encourage despair. I see that happening to me.

My H confessed as well, but he thought and still seems to think that once you've confessed and been forgiven, that's all you have to do and you can live your life. He thinks that it's a lack of belief in God not to trust in His mercy and forgiveness.

He is correct.  It's a grave sin to doubt your forgiveness in the confessional.  
Also he was given penance by a priest.  You don't have the authority to impose further penance upon your husband by withholding the marital act because you "feel" it's the right thing to do in "your heart of hearts".  

I sound harsh, but I applaud you for this wisdom -

Maybe this continual unhappiness and torment IS the penance I am to uncomplainingly pay and maybe if I can master never expressing it or trying to make my H understand, it can be meritorious.

Please ONLY allow him to see your love.  Don't ever indicate repulsion. That's sinful in itself.  You both confessed, did your penance, so get on with serving God each day in your duties of life.  If you feel the need to do daily acts of reparation, bravo!  God will be very pleased. Perhaps that can include daily acts of extra kindness and love toward your husband.  

Advice from a priest to a soul who had a sterilization: "imitate Our Blessed Mother and spiritually adopt all you encounter"  
There is no coincidence to those we meet each day, so make everyone your child, praying for their souls.   What a magnificent way to make daily reparation.

All in all, it's best for you to make an appointment with a traditional priest to discuss.

Just a quick clarification, I referred to the purposes of the marital act, as separate from the purposes of marriage.  I've read before that the marital act begets children and protects the spouses from concupiscence, i.e., temptation to adultery.  If the act is not performed, one or both of the spouses may be tempted to find participation elsewhere.

I received baptism/first communion/confirmation as an infant in one of the orthodox churches at my grandparent's request.  I attended services occasionally throughout my growing up years and quit going at age 16.  I did not receive any instruction in the 10 Commandments, had never heard of Sacraments and basically failed to receive much of anything in the way of what it means to be a Christian.  

I was woefully mislead for years about the need to do anything different with regard to practicing the Faith ... allowed to have a Nuptial Mass and receive Communion as an Orthodox ... was never talked to about Confession.  Nothing.

I have confessed this sin since my conversion. The penances given by the priest are incredibly mild and I know also that even if they weren't we're still called to practice mortification and penance for the rest of our lives.

I appreciate the suggestion for spiritual adoption.

 I also understand the continued recommendation from poster(s) to foster / adopt children.  Not everyone is called to that particular act of charity. It's lovely. It's admirable.  But not everyone has what it takes due to age, resources and state in life to accept children into their homes in that capacity.  

The fact is, not all children needing fostering can or will be adopted.  Many of them will in fact be returned to their homes, God help them.  It takes a special grace to be able to provide housing and guidance to children who have been sɛҳuąƖly abused, living in drug addicted homes, and all the other things that go on in this foster care cases. It's a great thing if that's what you are called to do.  Not everyone can or should do that.  

Finally, I do not have access to a traditional priest.  We live 4 hours from the nearest traditional Latin mass parish.

Which state to adopt?

St. Mary Magdalen did penance for years -- until the end of her life. As did many other saints.

That is the way of the saints.

The saints did penance for their own sins, and God can apply that penance to other souls if (objectively speaking) the saint is already "paid up".

Pride?  Maybe a pity party with ones self?  Feeling sorrow for ones self?  What NFP, excuse the secular phrase, but what they were trying to get to was to create a new interest/personally with husband and wife.

For example:  Couples who can not become pregnant, feel like they are going through motions of sɛҳuąƖity and lose their desire for each other as persons.  So, couples like this, tried only having relations during the fertile time and wait on the infertile time.  They saw a difference and a new interest with each other as persons.  So, the suggestion is well to take.  

Then see if there is something you can do for the children of the world.  There are parents with "special" children who are not able to get a time out.  There are babies of drug mothers who need rocking and held.  Give that some thought.  Maybe you see a family and they have needs, maybe help for Christmas and or throughout the year.  You start and see if your husband wants to get in on the gift of giving to others.