I have to revive this post, because i was struggeling with the same problem and i think i found the solution.
The cause of the problem is the setting:
CommonUI.ShouldVirtualAcceptSimulateMouseButton
If you deactivate it with (standard is true):
CommonUI.ShouldVirtualAcceptSimulateMouseButton = 0
the Gamepad Face Down Button is not simulating a mouse click anymore and the implemented input action for the Face Down Button is working correctly.
Edit: I just saw the console command got added in UE5.6
For versions <5.6 the only solution would be to override ShouldVirtualAcceptSimulateMouseButton in your FCommonAnalogCursor class