It's the corners that kill it
I can kind of see what you were thinking when you made that rule, that corner pieces can only be rotated relative to their connected sides, but that really needs to go. I started a Survival game, and the entire lower half of the board was rendered unusable by a single long twisting line of corner pieces that came pre-connected to each other, not quite in a chain or a loop, yet completely immovable. So I went to try Time Stress instead, and died on Level 1 after only a dozen blocks, because most of them ended up falling over one single column, and hey guess what, more corner pieces that I can't move. Argh.
There's the potential for a pretty good puzzle game locked up in here, but as it is, getting the pieces together is almost entirely based on dumb luck rather than thoughtful strategy.