There is prepping and there is prepping. Right now I'd say the notion is in the "Let's kick this around and see where the easy and hard points would be" stage.
Ignore petitioning for redress of grievances? No way - although I'd appreciate hearing just what your grievance is at this point. Sounds to me you are more at the "expressing an opinion" stage.
What to do at this stage of the game? Start by making your congresscritters (all 3 of them) believe they will be better served in the long run by not just supporting S.2002 but amending it such that a person caught up in the executive fiat does not have to go through a judicial and then administrative process to get back to
status quo ante but has their record expunged unless there is documentation of the type of hearing Cornyn says is needed to put them on the NICS program to begin with.
Start working on the publicity/PR campaign to not only counter but smear CCGV, Brady (what's left of them), Everytown, Moms Demanding Attention, Bloomberg's money and Bloomberg himself. Not countering their BS with facts, but smearing them the same way they are smearing us. The gloves come off and the truth comes out.
In your particular case? File for both temporary and permanent injunctions against Social Security submitting your name to NICS until/unless you have been through the judicial process required by law. Find out who else is under similar threat and create a class action.
I'm not intending to be mean or nasty or even snarky (although those are my usual and natural states) but I remind you that your question was
My question is this: if legislative efforts fail to stop the adding of Social Security recipients with rep. payees to the "can't buy guns" list, what sort of judicial options would someone like me have, given that I've not fallen into any "prohibited persons" category previously?
You did not ask what you can do to stop the process
before you got caught up in it. I gave you he best answer I could come up with that did not involve parsing both the executive/administrative directives, the agency(ies) guidance to the field on what to do and who to do it to, and S.2002. I could do that for you but it would entail a) at a minimum 90 days and b) also at a minimum an advance payment of $10,000.00 and c) a non-disclosure agreement to protect my investment of time and cogitation from being diluted by having it spread around to others who are not willing to reimburse me for my efforts. (And no, I am not holding myself out as a subject-matter expert on any of this. I'm just some guy who can usually wade through bureaucratic BS thanks to both education and professional training in doing that sort of thing.)
OTOH, it would require nothing more than asking me to throw whatever I have to offer into developing and moving forward a class action.
stay safe.