AA is not an EU carrier and the last time I looked, Philadelphia was not in the EU. Thus, EC 261/2004 has less than nothing to do with this.

The correct pricepoint here is the US rule which would require a cash payment of 400% of the segment fare capped at $1,350 (+ hotel & food). Presuming that the segment fare was at least $337.50, each passenger if IDB was due $1,350 in cash (or equivalent).

But, OP accepted a VDB. That is purely a negotiation and a reverse auction. I have recently seen AA pay $1,000 (in vouchers) for micro-haul commuter runs and also seen $250 for 4 hour flights. It is up to the passenger and if no passenger grabs it, then the offer might go up.

I see the baggage issue as a separate customer service fail having nothing to do with the VDB issue. OP was apparently told that his bags would be offloaded and that he might claim them at baggage claim. But, they were not. Thus, OP should purchase necessities and keep the receipts. He should submit those to AA after the trip with a note explaining that AA had said it would but did not offload his bags.

I give this gambit about a 33% chance, so OP should not spend what he would spend if he knew that he would not be reimbursed.

As an aside and having nothing to do with IDB/VDB, bags get lost and other things happen all the time. Given AA's generous carry-on allowance, I would always have 2-3 days clothing in the carryons.

The US does not require offloading of bags and has not since 2003, when 100% of checked bags were screened. It is up to AA to have a policy on this and I suspect that this was not a situation requiring that the bags be offloaded.