Halo bassinet and 11 week old

My son is 11 weeks and wiggles and pushes himself to the edges of the halo swivel bassinet and I’m getting worried that he can push and turn his head up to the non mesh part at the top and bottom. When did any others move their little ones out of the halo bassinet? My husbands not ready to move him in the other room and our room is too small for the crib. We could transition to a pack n play I guess, I just don’t want to make transitioning more difficult for the lo