Off the top of my head, from my local knowledge; if you have time to spare; I'd get the cheapest flight available to TPA. Then AA in first TPA-MIA-LAX R/T; which is 540TPs for about $1200. Also, by choosing a 763 for the MIA-LAX-MIA, you'd get a great travel experience: far surpassing CE.
It's time-consuming; so may not suit you and it exceeds your TP requirements. It's just a thought.