Only you can decide if him not meeting your request to destroy the picture is a deal breaker or not.
You want to move whether you live with him or not so perhaps making arrangements to live on your own is best use of your energies at this time. You can keep dating him or not date him without it affecting your living space that way. You can wait to decide that way too.
I would focus on moving closer but not in the same home. Sort out where you will live first. Then deal with the boyfriend problems.