I'm sure you'll know best how to approach your H about getting tested, just be careful on how you go about it
As for his crying wolf about moving out....just curious. Have you ever looked at him and said "put up or shut up!" Literally, tell him "Look, unless you are REALLY going to do it don't bring it up....it's a threat, it's not working and I don't believe you....so put up or shut up."
