Here's a line to stick in your back pocket and possibly use next time he suggests moving out but getting an apartment in the same complex:
"Oh H, do you really want live where you'll see my new boyfriend coming and going from the apartment?"

And when he says "wait, you have a boyfriend??" Tell him "no, but a good woman like me won't be lonely long. If you're going to date I think I should too".

It seems ridiculous, but most WASs have not considered that what's sauce for the goose could be sauce for the gander. They think you're going to be waiting as Plan B rather than moving on with another man, and the thought of you dating too upsets their fantasy.

(Bear in mind, I'm not suggesting you date...but H doesn't have to know that, right?)