Before travel

1. Call BA to to get on the earlier AA JFK-LAX flight.
or
2. Call AA to get on a later AA LAX-DEN
or
3. Call AA to get a refund of LAX-DEN-LAX.
Shouldn't be too hard to find an understanding agent given the fact pattern.
A nice option here is to rebook the LAX-DEN segment on UA for ~$250 one-way in F with LAX-DEN-BIL.
that would get you a mainline UA jet rather than an RJ, avoid the Eagle's Nest

Day-of:
My experience is AA allows free confirmed stand day change for paid & upgraded first class. Logic suggests this would also apply to paid & upgraded business class. I know it does not apply to saver award first class.