What are to tallest and most agressive mud tires I can fit on the stock praire rims?

Stock tires are

Front AT25X 8-12
Rear AT25X 10-12

 

dont know for sure but I think 27's will work, but be forwarned, the 360 certainly is no power house, anything over stock you'r going to loose power.. I put some oversized 589's on my old P-300 that damn thing would hardly move..

 

I have a 99 prairie 300 4x4 that had the same tire size as yours. I am using 26" ITP 589s with a lift kit and I am not having any rubbing. I am pretty sure they would fit without the lift. The 300 cc atv is already slow and I did not notice a speed loss due to the larger tires. Speed is not one of my primary necessities for what I use this bike for. You can take a look at my pics to give you an idea of what the 26" look like.

 

I have 27x9x12 589's all the way around.. I put the 9" on the back to save on the power and they do great. Also put a Dyno jet kit, and a black secondary spring.. Its not fast but it does the job.. Any bigger that that I think you will loose lots of power and won't be able to turn them over when you really get in the mud!