Cannot tell if the OP is on the final return leg of the AA ticket. BUMP would only work if that were true since AA will cancx out the remaining legs.
Yes, very difficult to use the BUMP with an AA ticket, but it can be done -- I pulled it off about 5 weeks ago. You will have to look for a TA sporting a old NWA badge or lanyard (and proud of it)-- probably a bit difficult in JAX!
The other challenge is getting your DL SM number in the record so you can claim flight credit later....