Also keep in mind that 13 is a Senior cat so it’s not that surprising that he’s a bit cranky. Everything around him is changing.
Cats don’t welcome change at all. If they could have their vision enacted of a perfect world for them, each day would be exactly like the previous. The only change they find pleasant is a variety of small animals and birds scampering about outside their favorite window.
Other than that, they want their favorite food, litterbox in same location, same napping spots, favorite human, other animal companions etc etc.
Any changes to those unsettles them. Right now you are his rock and his safety. Being able to cuddle up with you each night and be able to nap on your bed and be in the room with your scent all over when you’re gone is what will help him the most.
I agree completely with keeping him in your room only for at least a week and possibly longer. An extra week or more probably wouldn’t hurt.
And when you’re ready to let him explore further try to do it at a time when you’re going to be in your room anyway. Just casually leave the door open slightly and allow him to go out and come back in as he chooses.
If he still prefers the safety of you and “his” room, that’s fine too. When he’s ready, he’ll do a little exploring. But always keep the door open so when he needs to retreat back to safety he can. Don’t ever shut him out. This way he has the freedom to adjust to the rest at his own pace. There’s no rush.
My Velvet was timid that way and I moved with her numerous times. But as long as she could cuddle up right next to me on my right, she was OK. It always took her quite a while to adjust but as long as she had her anchor (me) she took it in stride.
The only times she was ever truly distressed is if I were visiting friends and couldn’t take her. I always had a loving cat person taking care of her but she wasn’t really happy till I came back. And she would stick to me like Velcro for about a week after.
But you should also try some of the calming natural products recommended by our other Fluther cat experts. Certainly couldn’t hurt.