Glad you discovered this. I've been using my one crooked tooth on the mouthpiece for 40 years. But it shouldn't force you to play on one side of your mouth. You should be able to play normally even with just one tooth. Perhaps something else is off with your technique. Sounds like the angle of the mouthpiece might be too steep (clarinet-like) rather than straight out. Do you have a teacher?One of my front teeth is longer than the other and I just realized it really affects my tone.
I've been working on loosening my embouchure, but it seemed to make my palm notes squeal uncontrollably. I saw a mention in a google search that uneven front teeth could cause this problem (because the reed gets pinched on one side) so tried only contacting the mouthpiece with one of my front teeth. This immediately solved the problem and made the horn easier to play across its whole range. My tone improved as well. I ended up playing in either the left or right half of my mouth - either way worked well since only one of my front teeth touched the mouthpiece. I'll give the suggestion to put a mouthpiece patch on only side a try.