If you want to fly on oneworld partners other than BA (and AB?), then you can call. For a trip like this, I'd spend the extra few bucks for telephone ticketing, but avoid BA because of the carrier fees. Personally, I'd take my chances with the 3-class 777 in F on AA and the direct flight, even if it won't be up to international carrier F standards. Any other oneworld carrier will require a connection (unless AB does DFW-FRA?) DFW- FRA might be a little too far for the 763 range, so you wouldn't have to worry about that particular downgrade, and as someone pointed out, if it becomes a 77W you still get the flat bed and possibly some miles back.
One last piece of advice; if you book F using miles, check your reservation frequently starting about a month before you leave. AA has been known to change seat assignments and on occasion, change class of service for international F travel, although judging by
anecdotal experience that has seemed more likely to happen on 77W flights to London Heathrow.
Finally, you can't use your AA miles for LH F, unfortunately.