Sorry for the double post. I tried resetting both the heir and the genie, tried wishing to free the genie again, formed a band and invited band members, invited her to a party, asked to be Just Friends, and raised the relationship back up to Best Friend and the conversation tone to Friendly. I got as many 'Ask' interactions out of the way as I could to make space for 'Ask to Move In', but it never showed up. With permission, I'm going to try going back to a previous save since none of this stuff is working.
EDIT: I went back to the previous save and that didn't work either. Maybe because he's had the same lamp for so long. He got it way back as a teenager to try to use the Love wish for his RI requirement. Oh well. Guess I'll have to get a new genie