If I understand you correctly, your gravity works while ship is not rotating? So WHILE the ship rotates, theres issues, but when it stops, everything is ok?
If so, could the sliding be because the rotation causes the character to accelerate, so theres actually two forces, gravity and acceleration because of centrifugal pseudoforces (or whatever they call them)?
In that case, try:
1. Increase friction between floor and character - you cant slide if friction is high enough (assuming the physics work correctly and its not some glitch)
2. Dont accelerate the ship too fast (even angular acceleration is acceleration)
3. Design the ship to minimize such additional forces (dont make ship long on an axis where it rotates fast)
4. Separate the ship-internal physics completely from the external physics AKA cheat. Like if a player enters a ship, spawn them in a stationary "ship internals" world that has not much to do with the actual ship doing crazy 30 g manoeuvres while you chill there. How to accomplish this depends on your tools.
If this is a physics glitch instead of a natural consequence of rotating the ship too fast, then you might want to read on known issues with whatever you are using, or how they work, to figure out why its happening.
Thanks a lot, I will try!