These types of rings do tend to pucker out of planarity, as you have described. You're exactly right that by breaking perfect planarity, the conjugation is decreased, thereby decreasing the anti-aromaticity of the system, and helping it to be less unstable.
However, due to the constraints on bond angles imposed by the orientation of sp2 orbitals that overlap to form sigma bonds, the ring can't just take on any shape it chooses to fully get out of anti-aromaticity. It will strike a balance between the energetic penalty of straining its bond angles and that of being anti-aromatic.