It is possible to transfer BA to IB.

See here:
https://awardwallet.com/blog/how-to-...ween-accounts/

But, I'm not sure whether or not doing so would get you better/different flight options.

I assume both have better availability than AA.com, but not necessarily more attractive pricing.

You basically should just do a little more research to make sure you cover all of your bases.

As others have suggested, your initial effort doesn't win much praise from the peanut gallery here; in fact, sub 1 cpm redemptions are borderline sacrilegious in these parts.

But, with a little bit of tweaking, you might be able to put your miles to decent (but probably not outstanding because your dates are fixed and rapidly approaching) use.