https://paste.dimdev.org/bibidabowe.mccrash

Pushing blocks into the drill works fine.

My current work around is adding the drills to Quark's S:"Tile Entity Movement Blacklist"

You're not supposed to be able to move drills with pistons. Quark allows pistons to move tile entities, they have a blacklist because this can cause issues with other mods.
I could probably fix this crash but I don't see the point in being able to move drills with pistons since they require a mechanical power source that would have to move along with them.

clearly the solution is to add a piston with an axle going through the backface :^)