The first thing I would do is load the game, but not launch it, and then disable syscalls (simulate ofw) before launching game.
If it doesn't solve the problem, its not the cfw.
If it still is a problem, see if there are any game updates for said game. If so, install them and test.
If the problem isn't solved, the only way truly to figure it out is to debug the game, which is a whole other subject beyond my comprehension.
They've had you test the controllers (which is kind of crazy if it works fine in every other game, but one). this isolates it down to the individual game. At least at this point we know it's not the controllers. You tried a diff firmware (rebug 4.81 and still same issue).
Recap:
1. Eliminate CFW as culprit (simulate ofw by disabling syscalls and test)
2. Check for game updates (they can solve bugs)