You can agree to vacate judgement as a condition of your payment.
If they agree to that then you enter a stipulation to vacate the judgment once its paid (to the amount you agree) with the court.
I did this once.
However, this will probably only happen if:
1.) You agree to a lump sum payment upfront. (most of time you can get it down 30%).
2.) Its not too far after the date of judgment.
Lawyers are hesitent to vacate if its years out.
So better to deal with it right away after it happened.
I would never agree to pay a judgement unless vacating it was part of deal upon payment.
If you are looking to vacate because you want to war over the issue....good luck with that. you will have to show court you were not properly served or had some excusable neglect. That is a tough road and probably not worth the effort. Your time to fight this is probably past.
Once its reduced to a judgement, its, generally, time to stop fooling around and look at some sort of payment negotiation. (Unless, you just want to grind the appeals into oblivion....that will not get you a deal to vacate if you do that...most of the time. But it sounds like you are past appeals deadlines as well.)
This is where the "do nothing" option can bite you. The "do nothing" in court option is always the worst option.
I'd BK them, or bite my lip and negotiate, pay and get them vacated in exchange for completing payment arrangement.
That's what I would do.