Welcome to the BA Forum Mike!
As already stated before, there is no disadvantage booking via AA/Expedia, if you donīt plan on upgrading via Manage my Booking on BA.com. Itīs just that AA has a different quote on the same inventory than BA has. As an example, I booked a journey BUD-LHR-JFK-LAX-LAS/HNL-LAX-JFK-LHR-BUD with LHR-JFK-LHR being AA flight numbers, but BA metal. That actually made me save almost 25% in First Class.

There should be no difference in the accrual of TP/Avios, because the only thing that counts is the metal youīre flying on and not the flight number. Unless BA made some recent changes to that, that Iīm not yet aware of.