You don't need to teleport past the spikes... you can cut the rope on the platform
This is turning out to be really slick. I'm impressed. I think the up-down-up-down key combo is a little excessive. Perhaps you could do a simpler control to activate it? It's not hard to do, it just seems like it's more key presses than necessary.
And I was able to teleport outside of the level (again
A tip... to keep from "replacing" yourself in a wall, have a dummy object go first, and if it's overlapping solid then run a quick push-out loop. Once it's free, move the player to the dummy object's location and kill the dummy. (You can tell which direction the dummy needs to be pushed by doing a system point collision test using it's top, bottom, and sides locations before running the push loop.)
But this is looking really nice so far, excellent work