I have had facial numbness as the primary symptom of my AN for a little more than a year now, though I have not yet had my treatment--I'm due to start FSR treatments this Monday.
One thing my doctor told me is that the numbness may never go away. Now, I'm not having my tumor removed, like you would have had during surgery, but if the tumor damaged your trigeminal nerve it may be that it might not go away, or it could take a while for the nerve to recover.
I'm certainly no expert and I'm sure there are folks around here to have more experience or insight than I do, but one you mentioned rang a bell for me.
I have noticed that when I'm well rested, first thing in the morning or right after a good nap, that my face and the inside of my mouth feel a bit less numb, a bit more normal. It certainly doesn't go away, but I feel that it's not as aggravating, especially inside my mouth and in my eye, which has been affected. My scalp feels less numb, my eye feels better, my teeth and gums feel less "off".
So, it could well be that the intense exercise is adding to how you feel and that making sure you get a good night's sleep, or taking the occasional nap may alleviate some of that.
I don't know that you need to "exercize" your mouth by chewing gum. I think that as long as you're moving your jaw when you chew, even on your unaffected side, that you won't lose muscle tone. I try to continue to chew on my affected side simply because I don't want to have more wear on my good side, and I just kind of ignore the odd taste sensations, but it's true that it seems easier to bite your lip or cheek on the numb side.
But try paying attention when you first wake up--if it's better then, maybe you can avoid over-taxing your body. I'm not talking about avoiding exercise, but simply making sure that you get plenty of rest to let your body continue to recover.
Good luck!