New strats from the TAS run. Level 15 was changed a bit, you can manually spawn 4 bears and try going for catapult.

I'm pretty satisfied with this, although many more seconds can be saved:

Level 6: 1-2 seconds, if one can enter into the wall in first try. Level 7: 1-2 seconds, with clipping into the floor at the beginning. I gave up on trying that. Level 8: 3-4 seconds, if one can manage to get down the floor in first try. Level 15: 2-3 seconds, if one can manage to get the bear catapult in first try.