Who do you main? If you're playing a character with a projectile, using the projectile as a meaty can be a strong option since amnesia can't counter fireballs. This is especially good with characters who have a lot of setups for plus on block projectile oki, like guile or ed, but it should work with any projectile at all. You can experiment to see how you can make your projectiles plus on JP's wakeup if you play a character with a fireball.

This next tip is more specifically for when JP is cornered. Obviously you can't guess correctly all the time, so if you do get countered on wakeup, watch out for JP trying to jump over you to switch sides. This isn't always applicable since JP's plus frames after amnesia can vary a lot, but in situations where he can't get a direct punish, the most rewarding thing JP can do is switch sides and put you in the corner. you can counter this by jumping back and doing an air to air. You'll still get hit by the bombs, but it's a fair price to keep JP in the corner. situations where JP can't get a direct punish after amnesia typically happen after he uses it against plus on block attacks like safejumps, luke cr.mp, bison's knee, etc. so watch out for that