This is an interesting Sokoban variant.
It would have been more fair to visualize the area of influence of each eyeball.
I agree that it should be a turn based system. It is much fairer to have a clear idea of how much you can withstand against an eyeball. It would also eliminate the need for precision manipulation.
About the level design. The puzzles in each level are all interesting, but they all have a level of difficulty that requires application. How about adding a level where the player can learn about a certain element or technique?
For example, in the second stage, as soon as the box appears, the player needs to work on its application problem (solving two eyeballs with one box). Subsequent stages are also application problems of Sokoban techniques and core mechanics, which are quite difficult for players who are not familiar with Sokoban techniques. This is because the player has to solve two or more new contradictions in a single puzzle.
Overall, I really like this game.