OP's sole obligation was to wait for the last bag off his flight. Once that was out, all he needed to do was exit Customs and head back through a checkpoint to his departure gate. I presume that he would have made his onwards connection (if it is a connection). EC 261/2004 does not apply because his flights were apparently on time and there is no coverage under the Regulation for baggage or Customs delays. That is also the end of any "duty of care" under the Regulation as well. DOT has no particular rule governing this, so that will be a dead end.

If one has a long connection, it may pay to wait around and figure out the bag issue. But, if the connection is looming, best to simply head to the final destination and deal with the bag issue on arrival.

Wherever OP was destined, I find it hard to understand why anyone would wait 8 hours to take a 1 hour flight. Is there no car, bus, train which would have put him at his destination sooner?

As to the bag, it will be for the final delivering carrier to arrange to have it delivered to him wherever it is that he is headed.