The vet had recommended keeping them in a bathroom during the move, one attached to a bedroom preferably if this an option that would less likely be used or attached to the bedroom where you will be sleeping ideally. Make sure to put a sign on it not to open so the movers are sure not to go in and let him out.

Then introduce him to the bedroom once the movers are gone and things are done being moved in and out, ideally by just opening the door if the bathroom is en suite so he can find his way. Keep him in your bedroom then for a couple of days to get used to it. Then let him move into the rest of the house.

I've always done this with mine and had pretty smooth transitions.

Wishing you all the best with your move. Congratulations on the new home.