There are some ways to cross up with the Devil’s reverse but I’m not really sure how to set them up. I think the hit box is wierd enough on that move so you can actually hit your opponent with your shoulder of your non-expected arm. In general, if you have the ability to cross up your opponent, yuo should really go for the: jumping forward kick, standing shrt kick x 2, low forward xx fierce crushaa for a dizzy (and a win). I use the Devil’s reverse to bait out moves, build meter and empty jump throw. If you do the Devil’s reverse and do nothing, it works at a sort of low jump where you can throw the second your toes touch the ground. It works as a good surprise tactic from time-to-time and you throw them so fast it almost looks like an airthrow.
You can also get the same airthrow effect after your opponent locks the head stomp and you use the punch button follow up to steer yourself near your opponent (preferrably behind them). I played an dictator player at More in Japan that used this “air throw” tactic with great efficiency.
Bison’s Psycho Chrushaa corner cross up works like this. Knock down your opponent (throw, scissor kick, etc.), do a roundhouse kick slide to get near them and charge back at the same time, as they get up do a fierce PC and continue to hold towards (which will now start your charge the on the other side), now do standing short x 2, low forward xx fierce PC to your opponent’s back.