Welcome to Flyertalk and to the BA forum TheSiloBlewUp. It's good to see you here, welcome on board.

I think you may have jumped to a few conclusions in your post. The one and only reason for what you are seeing is that BA redemptions match directly to MileSAAver awards. If you map the AA availability on MileSAAver you will find that for many dates in August AA is currently only offering indirect routes. Nothing new or strange there, in August redemptions get harder to find, and all paths as to why that would be lead to AA. Have a look at 5 September to see direct options between MIA and DFW, for example. It may change later on, again subject to AA's take on revenue management.

Your other option is to go FLL-DFW, for which there is some availability, e.g. a choice of flights on Wednesday 21 August. 7,500 Avios and £4.30