What does his routine look like at the moment? Wake up, bedtime, naptime & length etc.
Eye teeth were the worst teeth for DD1 besides the 2 year molars (and those more due to sheer time than pain!). But not so for all kids, DD2 & DD3 (she is just getting all 4) seemed to be fine with those.
Personally I would be wary of taking her to other rooms during a nw as you are kind of setting the stage that she gets to decide what happens...but it does sound like if she is happy to leave her room that she may be undertired.