Personally i would.......a change is as good a time as any as they say. Big boy in a big boys room and all...... I think what your doing is a great idea (involving him in the process). He sounds like a good little man, with support from you, i would do the whole move in one go. There maybe teething probs, the first few nights he maybe a little unsettled, but with repetition and support, within a week he should be okay.
Thats what we found anyway. We did the big move when DD was a little older (28 months), new bedroom, new bed. She did the transition really easy, it was like a little adventure for her......
Good luck.