So, my 2001 300EX has 22" GBC Dirt Devil AT rear tires. The fronts are all wrong. They are bald on the center and are too flat (wide) and they don't hold air. Since my rears are somewhat oversize would one need to go with 23x7-10 instead of the 22x7-10 that is on there? Are the Goodyear tires that several folks have for sale on eBay for 120.00 delivered for 2 a good tire? like Like this pair

 

I don't know what the dirt devils look like but the ones in the link are more for loose dirt or sand they will not provide braking traction as well as one with off-set lugs. They also will not track as straight as an off-set tire because the lugs will flex sideways and cause the tire to walk. None of this applies to sand because the physics are different.

IMHO you should never have more traction (tire) in the rear than the front. It is to easy to get yourself in trouble by outdriving the front suspension.

Having a 22" on the front and a 22" on the back is fine, just set your preloads (ride height) for the new tires and the attitude of the quad should be close to the same. A 23" tire with the same width will flex in the sidewall more making it feel wallowy compared to before.

A flat bald tire is a long way from ANY new tire. Handling will be all different because the tires have been changed.

 

Front tires on a 2wd sport quad ususally work best with a straighter pattern for steering control, like Fast Trekkers, Razrs, Holeshots, etc. Dirt Devils might be a bit heavy and aggressive for a smaller engine (282cc). If you need that aggressive of a tire, maybe a Mudlite SP (sport) would be best in back, or even a good set of Razrs or Holeshots would be a better all around tire. I don't know what your riding area is like, mud, trails, rocks, that will affect the best pick for the tires you need.