Stapling can no longer happen under federal law, so the US FAs and the AA FAs will either agree on seniority integration or an arbitrator would decide.
I agree with you that Parker is playing the AA unions, but I also think that they are playing him, hoping that cuddling with Doug Parker ultimately gets them more from AA. I seriously doubt that any AA employees actually want to merge with US, as airline employees generally despise mergers.
This is Parker's last chance to be the CEO of a world-wide airline, and he knows it. He's willing to spend whatever it takes, even if it means promising the AA employees the moon (which would be funded by the current US employees, no doubt).