There are a coupe of inherent issues you will come across building off the demo. It will require some original thinking.
First, I would change the game so the player is only running while "intouch". You'll find that getting stuck in the blocks happens a lot less. I have no solution. I treat it as certain death. I make it a playable glitch that became part of the game. Very rarely the player can escape. I do some things different in my game. I destroy the player outside of layout. My player has a range of motion across the screen. You might try making the player solid but, I think I tried that. Or make the spitebox longer height wise and solid.