A fun and practical idea you guys have here, I've enjoyed seeing the different solutions people have come up with - I'll tell you my own under-$500 solution after the ban sunsets, but for now I'd better keep it to myself...
I have a suggestion that might make things even more interesting:
Remove the requirements that parts be new. You could probably stay under the $500 ceiling more easily if you allowed buying surplus parts such as GI M16A1 uppers, furniture, etc. Keep it fair by requiring all parts be advertised for sale to the public in a legitimate publication such as Shotgun News, Gun List, etc., or from an established e-vendor such as Bushmaster, Fulton Armory or whatever.
Must be sold by a company, not an individual at a fixed, advertised and therefore verifiable price. No auction stuff, since there's so much variation in price.
OTOH, now that I think about it, auctions are real transactions available to the public and are verifiable by their item number, and if you're really shopping hard on a budget perhaps eBay, Gunbroker et. al. should be allowed? Well, that last suggestion is up to y'all to decide. Just thought I'd make some suggestions to help make it more fun.
Might allow a lot more for the budget.