4) For this specific purpose (i.e., the transmission of sanctifying grace), if there is a sacrament + well-disposed communicant = grace passes.

You are taking a general principle and applying it to circuмstances which don't make sense.  You are leaving out all kinds of factors, which affect the morality of the situation.
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A valid baptism gets rid of Original sin, but is it a good and holy baptism if it is done in the middle of a rock concert, while Ozzy Osborne is on state screaming blasphemies?  Of course, this would be an abominable sacrilege and the participants would commit a heinous sin, even if the sacrament were valid. 
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Going to mass provides grace, but am I allowed to show up to mass in pajamas, half-naked, and approach the communion rail as if nothing is wrong?  Of course, this would be a sacrilegious scandal, even if the communion would "provide grace".
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A priest has the power to walk into a grocery store, go to the produce section, setup a table, and say mass.  Is "grace conferred"?  Yes and no.  Yes, in the sense that the mass would be valid, but no, in the sense that this act would be highly illegal and immoral because Church Law would forbid it and also such an act would be a sacrilegious and blasphemous use of his priestly abilities, taking no account of the reverence of Mass nor of the glory due to God by a proper church and liturgy. 
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The circuмstances of an act, even if the act is a sacrament, affect the morality of the act.  This is philosophy 101.
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Pax has now invented a new invalidity of mass "communion in the hand." Wow. What part of the mass is communion in the hand? If a person receives kneeling and the next person receives standing does Jesus disappear because mass is now invalid?

Many of you are falsely viewing this debate through the lens of validity only.  You are obsessed with this litmus test and ignoring all the other factors.  Even if the new mass could be proven to be 100% valid, every single time, one could still not go.  Because of the illegalities of the liturgy (which make it gravely sinful) and of the overall atmosphere which is anti-Catholic, irreverent and immoral.  Communion-in-the-hand is a sacrilege, because only the priest's consecrated fingers are allowed to touch the Holy Eucharist.  Communion-in-the-hand happens at 98% of every single novus ordo mass across the globe.  Therefore to attend such a liturgy, where this sacrilege occurs on a normal basis, is also a sacrilege because one is not allowed to attend liturgies which allow sin.  You would be openly and publically condoning this practice by your attendance.  This is not to mention all other other, varied sacrileges (talking, dancing, women altar girls, women/men Eucharistic ministers, dogs in the sanctuary, homo/gαy services, immodest attire in the sanctuary, etc, etc).  Validity, while an important question, is the least of the problems with the novus ordo.  If you think you can go to any valid mass, while all the above nonsense takes place, and think God is honored and glorified with such anti-religious and anti-Catholic activities, you just aren't thinking like a catholic.  At all.

“It must be understood immediately that we do not hold to the absurd idea that if the New Mass is valid, we are free to assist at it. The Church has always forbidden the faithful to assist at the Masses of heretics and schismatics even when they are valid. It is clear that no one can assist at sacrilegious Masses or at Masses which endanger our faith.…

Here it is again, Sean.  Read it a few times and let it sink in.  +ABL is not in your corner.

If you couldn’t refute my position by now, I have no worries you shall be able to do so in the future (particularly since my position is the position of Archbishop Lefebvre).

Your liberal position has been repeatedly proven false, but it is exactly that - your position. Have another beer.

Uhm, I already made the distinction between going to Mass vs. receiving the Sacraments.

If I am dying in a car crash, and a schismatic heretical priest can hear my confession, am I obliged to withhold making it??

Confession is necessary for salvation if one is in mortal sin; mass and Holy Communion are not, to the same degree at all.

But Catholics can “never” participate in, or receive, sacraments from heretics or schismatics.

Canon Law allows schismatics and heretics (even atheists) to provide baptism, in cases of necessity.  Heretics/schismatics can also hear confessions in emergencies.  Don't think that Holy Communion is allowed in the same sense.  If it is (and I'm not sure), the liturgy would have to be catholic and moral and valid.  The new mass is not catholic or moral.  That's the difference.
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Even in cases of necessity, one cannot commit a sin against Faith, to receive grace.  If you were dying and a heretic priest came to you and said, "I can hear your confession, but you first must admit that Our Lady committed at least one sin."  Or, "I will hear your confession, but you must say that the Patriarch in Greece is just as important as the pope in rome."  You can't do that.  In any way, shape or form.
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In the same way, the novus ordo is a new religion, with V2 heresies as part of its new theology and new liturgy.  Ergo, to attend it, is a sin against Faith.  Even if you skipped the entire mass and waited in the lobby until Communion time, then received communion, then left immediately, this would be wrong.  You are not allowed to scandalize your fellow man by participating (even slightly) in a "mass" which is contrary to Catholic theology and against the 1st commandment, and illegal, and immoral (since others would be receiving communion in the hand right next to you).  You cannot commit a sin, to receive grace.

Me and my husband were both born into the novus ordo not even knowing about the TLM or true faith...God did however  bring us to the true faith and the TLM and the knowledge understanding and practice of many aspects of living the faith. I do not agree with Fr. Hewko on this point but I think that people tend to be too hard on each other in the fact that each person is trying to follow God and the faith to the best that they can...we no longer go to any novus ordo mass or parish however because there are many heretical beliefs within the conciliator church. we believe it is a danger to a persons soul. 
So my main points are that we love Fr.Hewko and believe he has a point but that no one can really definitively state that no grace comes from the novus ordo because God in his goodness mercy and love can bring a person to the true faith no matter where they are.

Me and my husband were both born into the novus ordo not even knowing about the TLM or true faith...God did however  bring us to the true faith and the TLM and the knowledge understanding and practice of many aspects of living the faith.

That shows you had good will and God rewarded your search for Truth with the True Faith.

I do not agree with Fr. Hewko on this point but I think that people tend to be too hard on each other in the fact that each person is trying to follow God and the faith to the best that they can.

Fr Hewko is not condemning those PEOPLE who do not yet know the truth.  He is condemning the new mass because it's wrong, whether you know it or not.  Condemning the new mass is different than condemning people.

..we no longer go to any novus ordo mass or parish however because there are many heretical beliefs within the conciliator church. we believe it is a danger to a persons soul. 

This is exactly what Fr Hewko is condemning - that the new church is a danger to the faith, for all catholics (whether they know it or not).  If they don't know it, then we must preach the truth and educate them.

So my main points are that we love Fr.Hewko and believe he has a point but that no one can really definitively state that no grace comes from the novus ordo because God in his goodness mercy and love can bring a person to the true faith no matter where they are.

In your example, you were not converted/convinced to leave the new mass because of the graces you received from that service.  God brought to your eyes the errors of this liturgy because you had good will in your heart and through your prayers (i.e. you corresponded with actual graces).  It has nothing to do with sanctifying grace.
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Actual graces can be received anywhere, always and by all - under they are dead.  You can receive actual graces every time you think about God, even if you're standing at a bus stop.  Sanctifying graces only come from the mass/sacraments.  No one can prove that the novus ordo offers this type of grace because it is not a mass and the communions may not be valid.  It is best to assume there is NO sanctifying grace, as Fr Hewko is saying.  If you assume the worst, and you instruct people about this doubtful issue, then they are more likely to leave this bad mass and come to Tradition.