There are so many good ideas on these forums! As I read, I keep getting more inspirations...

OK, the displacer would work fine, but an even better method uses a positive displacement pump, driven by a stepper motor. (I'm assuming the drip system is far more precise than the pump, but the pump is sufficiently precise for pumping repeated volumes.) At the end of the slice print, the flag signal opens the solenoid valve and the drip system begins adding brine to raise the resin to the level of the next slice. Meanwhile the pump is also adding brine by a precise number of revolutions. When the drip count is complete, the excess brine has caused the resin to cover all the previously exposed slice. The pump is then run in reverse by the same number of revolutions, returning the resin level to the height of the next slice. A short pause would allow any movement of the resin to cease before the next slice is scanned.

However, if the stepper-driven pump is sufficiently precise for positioning the resin from slice to slice, the pump can replace the dripper system. It would raise the resin enough to cover all the previous slice, using X revolutions; then lower it to the level of the next slice, using -X+slice revolutions. I think this could speed up the printing process significantly.