There is a cable that goes from inside the transmission to the throttle body.
When you step on the gas, it pulls the cable, which increases the internal pressures in the transmission.
What I would like you to try is to adjust that cable and see if it improves or solves the problem.
This picture is for a Tercel, but it's the same. At the end of the boot, there should be a 1mm gap between the end of the boot and the metal collar when the throttle is all the way to the floor.
If it's less than that, adjust the two nuts to get it in adjustment.
If it's already at 1mm, adjust the nuts until it's 3 mm and test drive the car.
It should make reverse slip less or stop slipping. Let me know if the other shifts are too harsh.