I can semi-see where your son is coming from. His dad is useless, so you're the only security he has. His room is his, and his safe-space.
You're asking him to give up his space, his home and his guaranteed access to you, and in his eyes, he gains nothing for the trade. You're asking him to give up the two things that make him feel safe in his place in the world.
You can see the benefits of the 'male role model' thing, but he can't, and he may never do. Truthfully, if your boyfriend isn't in a quasi-stepdad role now, six years in, it isn't going to happen just because they're living together. At your son's age, their relationship is more likely to be driven by resentment than gratitude, I think.
I'd be very wary that the up-and-down isn't actually the 'he's happy/he's not' thing it appears and is in fact 'I'm not happy but sometimes I can pretend because I know you want it and I love you and sometimes I can't'.
I agree that children can't expect parents' lines to revolve 100% around them, but - particularly this year with all the other disruptions to his 'normal' - this might be too much.
If you are going to do it, it absolutely needs to be to a new, neutral space for all of you, with both boys a part of the process on equal terms and given free reign to decorate their own rooms till they're happy. Asking him to move in to your boyfriend's house is setting him up to fail. He's on the absolute back foot from day one, the tag-along invader with no comfort zone and no security. They already live there; you're moving in with your boyfriend - why's he there?
On a different note, if you are giving up an owned property to move into his rental, I'd be very cautious about how you do that. How easy would it be to reverse that decision and get back onto the property ladder afterward?