Rear tire uneven on my motorcycle?

My rear tire has a bead protector and it's not allowing about 3 inches of tire sit on the rim. So, the tread is uneven and if I go about 30mph, it feels like I'm riding a horse! haha

Anyway, how do you think I should fix this? I was thinking about cutting the tread down where the tire is a little raised so that it's all even. Would this be good?

I have knobby tires, so I would be shortening some of the knobs.
 
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