Here's one way to look at it. Whatever surface they are using, if you give away a ball that can be driven aggressively, that ball will have pace and could be troublesome to you. You could hit to that surface and get the player to give you what you want, even if it now troubles you.
I can think of three balls you give an a player using LPs or anti that he can hit hard back at you: An underspin to the LPs long that he punched of hit through to make a fast weak topspin drive, a high underspin near the net to either surface that he hits at a little les than smash pace, or a drive to the anti that opponent countered to make a medium fast or fast weak topspin drive.
Also, ANTI and LP players can hit what SEEMS to be hard balls on other shots, but they are actually medium paced shots taken off the bounce that rob you of reaction time making them seem faster. Any player with inverted can make the same off the bounce shots too, so such shots ought not be new to you.
In each case, you gave opponent a ball he can do something aggressive with, you know what his surface does, so instead of worrying about what is coming back, you should concern yourself with what you WANT him to give you and give the appropriate ball to them. You know what the ball will do, what its pace will be, how it will fly and bounce, as it shouldn't be a surprise if you give the player the ball with the purpose of ALLOWING him to hit what you want him to do... you are prepared for this and have options based on what you are allowing him to do.
Case 1: LP player aggressively hits through or punches your long heavy underspin, and creates a pretty fast topspin drive that is medium, weak topspin, or pretty flat. If you want the opponent to NOT make as fast a shot, do NOT make the underspin heavy and do NOT give the ball high. Make it as deep and low as you can. You have to know what your opponent likes. Naturally, crosscourt has the longest distance and best possible landing percentage for opponent, but LP players do not automatically hit crosscourt. They love down the line punch shot for winner if you give a higher and heavier underspin. If you want to slow down your opponent's attack on such a ball, give a very weak cut long and low as you can, there is a physical limit to how hard opponent can hit the ball and still land it with high percentage.
You are looking for opponent to make a semi-fast weak topspin. do NOT close blade too much. Use a shorter stroke if you are closer to table. Hit through the ball to one of the three best spots: Wide FH, opponent's small triangle (playing elbow), or wide BH.
An anti player can also hit an underspin in a similar manner.
Case 2: You gave up a high underspin that bounces near net or middle depth. Dude, you are toast giving away this ball to an inverted player, so don't sweat it, just read the spin better and make your underspins go deeper and lower and you take away this kill shot.
Case 3: You hit a drive to opponent's anti, he countered strongly a step from the table. Anti player needs to be a step away from table or so to help him use gravity to pull the ball down. He can hit a pretty hard shot that is flat or weak topspin. To slow his shot down, do NOT hit it high, do NOT hit it with weak topspin. An anti player can hit a no spin pretty well and make it a weak topspin. Like in case 1, anticipate a somewhat fast shot that has little topspin, be sure to open the blade and hit through the ball. Jamming the player by hitting it right at him is a very good option. So is hitting it to wide FH and going aggressively to the open BH side on next ball.
Each case you are limiting the opponent's aggressive shot towards something you are anticipating and ready for.
If you do not become comfortable in understanding what your opponent's surface does to your shots, then his shots will forever trouble you until you learn and control what you give him. Getting there takes some learning, practice and failure in matches. Once you get to a point where you are comfortable in hitting to the LP or anti to setup a shot you want, you are on your way to dictating the points in a match vs them.
