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It looks well polished and it was fun to play, although the randomness may end up in situations where it's impossible to finish the level.

Indeed. Perhaps it will help by adding extra vertical force to the cells when they are at the sides for 3 seconds.
 (either into or out of the sides will do, as they will bounce back) .

Not saying that the invulnerable spaces are not good. 
(It adds strategic considerations of allowing cells to get through the defense line or not)
But letting cells stay there for 5+ seconds without any signs of coming out can be frustrating