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:
1) if the SSPV chapel in question has Confessions at any time OTHER than before Sunday Mass, just go and do a general Confession during that time without speaking to the Priest about it beforehand.
2) As mentioned in a previous response, if you can get to an SSPX Ignatian Retreat, making a general confession is part of the retreat, so you could do one then.
3) If any SSPX chapel within driving distance is going to have a Parish Mission preached by Fr. Alphonsus María (SSPX Redemptorist Priest) anytime soon, he hears general confessions during his retreats.
4) As you yourself mentioned, you could just make a general confession to an SSPX Priest at the chapel you currently go to. If you're uncomfortable with that because you've already spoken to that Priest about why you want to make one, are there any other SSPX chapels in the state you could make a road trip to for a General Confession? Just tell the Priest you want to.make.one without mentioning the reason.
5) If your SSPX chapel or one you'd be comfortable driving a distance to has Confession times other than before a Sunday Mass, go and make a General Confession then, without making arrangements beforehand. In reality in this type of situation you don't even need to tell the Priest in the Confessional you're making one. Just tell him all the sins since your last Confession, and then all of the rest after that.
If the video of your Novus Ordo baptism shows everything was done correctly, you don't have a good reason to doubt it was valid, and neither does the SSPV. You're validly baptized, and if you've been making regular Confessions to SSPX Priests for the last year that you've been going to Mass there, you've been receiving valid absolution as long as you've confessed all of your known mortal sins since your last Confession, and have true sorrow, purpose of amendment, etc.
Additionally, you're always free to mention a SPECIFIC sin or two from previous Confessions in a regular Confession anyway, especially if in your current Confession you have nothing mortal to confess. So, if there is any specific sin(s) from previous Confessions you want to mention, just do so when making your regular Confession. Just specify these are already absolved sins.
If the SSPV Priest(s) you've talked to have met you in peson already, they probably won't let the matter rest without going through with instruction and a conditional baptism, and being they know your face, they probably would refuse you Communion (not certain of this though). But if you've only talked to them on the phone or by email or something, just make your General Confession through one of the ways described above, drop the baptism/confession preparation with them, and go up to the Communion rail and I don't think you should have a problem.