The ones who flip the bat are TWIDDLING and a good player who can twiddle and use inverted to punish your weak ball you intended for the anti can be a nightmare for you.
The best defense is a good offense.
There is no ONE thing I can say, because I do not see this opponent of yours.
However, there are a few things that may work. You will need to be consistent and solid enough to make them work, or they will fail with errors.
As Cake sez, I really like the idea of spinning the ball. Especially deep. Everyone has problems with that. To do this, you have to be able to get an underspin long. You will need to see long serves and spin them OR... you gotta give an underspin ball to get one.
What if he twiddles and loops the underspin you gave him? Block it wide and stay in the point look to counter attack.
Why did he attack your push? He saw it coming. Be quicker and faster. Push off the bounce right at him DEEP right near endline. It takes a good level to do that with quality and consistency, but that is the ball you need to give him to setup your offense. Push deep and fast and watch him just bump it back... then you get to go ballistic on attack with spin then slap it.
Another thing you can do is to vary the underspin you give him and allow him to attack, often it will be long and out when you pull the carpet out from under him and take off the underspin while still making it look heavy. Give him some really heavy balls to establish your underspin as heavy, then start giving him near-float balls. Watch his consistency go down the tubes !
Another idea to do is to make him MOVE. Do your underspin return, but at last moment, open or close the wrist and send the ball wide, like to his wide FH, even if he successfully attacks it, he had to move and he likely wont get back in time, so block it to his now wide open BH corner... if he gets that back, the shot will be weak, crush that weak ball for a winner and smirk Ur way to the scoreboard.
If you have the control, then giving him short return, and occasionally a BARELY long (thee are called half-long) this will cause him to be uncertain and hesitate to attack, likely giving you a change to attack and he is already in Oh-Shyt mode making it better chance to win the point.
You could also try to hit some balls faster than he wants right at his crossover, that messes up a lot of players, but some players are really strong blocking a ball to their crossover, so you gotta learn who he is.