If the meshes are static you can simulate in-game physics with them.
I was agreeing with kamrann’s previous post about physics simulation.
Alright, wait, you said four sides.
Are you enclosing the player in a box-like shape (one wall coming from the north, one from the south, etc.)?
Then again, I still go back to just using a trigger that will translate the player.
It seems there is a collision problem and this seems like the easiest option.
~ Jason