I suggest you contact a CMRI priest if one is available.  I don't think you would be required to do any of this.

https://cmri.org/cmri-directory-of-traditional-latin-masses/

If you went on an Ignatian Retreat with the SSPX, you could do a general Confession on the retreat. 

If you have your baptism on video and the form and matter seem legitimate, there is no reason for them to ask to have you conditionally baptized.  I agree with the others who have said here that you should just ask a priest to do a general confession for you.  

One does not need a reason to make a general confession.  You can make one at any time ... provided you don't intend to be in there for, oh, 30 minutes during a normal Sunday confession line (so the issue there being practical).  Scrupulous individuals are generally advised to avoid general confessions ... as they tend to make them regularly, always wondering if their past confessions were invalid.  But your reasons seem to be legitimate doubts about the validity of NO Orders, which the SSPV agree with.

So the holdup here seems to be the question of the Baptism.  I don't know of any Trad group who seriously doubts the validity of NO Baptisms provided proper matter & form were applied.  So I'm not sure what's going on here.  Seems like a bunch of nonsense.  If it weren't for your video of the Baptism, I might recommend a conditional Baptism in that it's not uncommon for Novus Ordite presbyters to play games with the form of the Sacrament, but if you have a video that demonstrates otherwise, I'm not sure what the problem is here.

Why not just schedule a general with the SSPX priest and just ignore SSPV ... unless they have legitimate reasons for suggesting that you receive conditional Baptism?  You need not explain to SSPX what your reasoning is for the general, as you don't actually have to have one.  It could be just for your spiritual benefit.  In fact, if you can do it quickly, you could probably do it in small pieces during your next few confessions.  At the end of your main confession, just pick either some categories of sin or some period in your life (however you want to break it down), and add some of these past sins at the end of each confession.  There was a Father Alphonsus who filled in for Father Carley when he had his hip surgery, and he was doing general confessions.  He announced from the pulpit that they need not take more than 5 minutes, as "there are only 10 commandments".  All that's required to confess is the category of sin and the number of sins committed.  And he was right.  If you want spiritual direction, guidance, etc. ... you can schedule that at another time.

Recall also that the invalidity of NO Orders is disputed and doubtful, so it's not of strict obligation to confess past sins confessed to a Novus Ordite presbyter, as there's no requirement to confess doubtful sins.  So this way you could just break up the confession of past sins into small pieces over time until you're caught up and you've effectively confessed your past sins.

Now, if there's anything in the video that suggests your Baptism may be questionable, that would be a different issue.  I'd love to hear what the SSPV have to say in terms of their rationale for doubting the Baptism.  Ever since the whole +Thuc issue, they've gone uber-scrupulous with regard to the validity of Sacraments.  They've gone down the "one hand" path and were conditionally confirming people who had been confirmed even by Bishop Williamson (because he was in the same ordination class as "one-hand Dan").

I suggest you contact a CMRI priest if one is available.  I don't think you would be required to do any of this.

https://cmri.org/cmri-directory-of-traditional-latin-masses/

Problem there is the distance, unfortunately. Looking at a 4+ hour drive. I appreciate your suggestion 

If you yourself have a reservation about the validity your Novus Ordo Baptism, and are looking to get conditionally baptized, going through some form of convert instruction is typically the norm. The length would vary by person depending on how much you already know.

However, based on your post it sounds like you're interested in a general confession, but not in a conditional baptism. In this case, you have a couple options:

Thank you for the detailed response. I do not doubt the baptism in the slightest, the minister of the baptism used the correct from with an infusion of water at each of the names of the Holy Trinity. They have not told me explicitly that I need to be conditionally baptized, just mentioned multiple times that it's the "standard" procedure.  I will probably feel it out for another week or so to see where they want to go with things, if it's going to be a drawn out process I'll go to an SSPX priest

I thought this thread was going to be about admission to communion since this is more likely where the SSPV is more stringent. 

I'm actually surprised by the SSPV response to your situation assuming your baptism was indeed valid.  It seems to me that if they are leaning towards a conditional baptism, the initial instruction in the Baltimore Catechism doesn't add up.  Are you sure they want you to be conditionally baptized?  And if so, what is their reasoning?

It may have been me just misunderstanding. Like I said above they didn't explicitly tell me I need one, just that it's what they generally do. 

One does not need a reason to make a general confession.  You can make one at any time ... provided you don't intend to be in there for, oh, 30 minutes during a normal Sunday confession line (so the issue there being practical).  Scrupulous individuals are generally advised to avoid general confessions ... as they tend to make them regularly, always wondering if their past confessions were invalid.  But your reasons seem to be legitimate doubts about the validity of NO Orders, which the SSPV agree with.

So the holdup here seems to be the question of the Baptism.  I don't know of any Trad group who seriously doubts the validity of NO Baptisms provided proper matter & form were applied.  So I'm not sure what's going on here.  Seems like a bunch of nonsense.  If it weren't for your video of the Baptism, I might recommend a conditional Baptism in that it's not uncommon for Novus Ordite presbyters to play games with the form of the Sacrament, but if you have a video that demonstrates otherwise, I'm not sure what the problem is here.

Thank you for the response. If they do try to go the conditional baptism route, which isn't clear yet, I will just go to an SSPX priest. I do understand that repeating NO confessions isn't absolutely necessary, but it would bring a great deal of peace to mind to dispel any doubts I may have.