I run 28" xl's on my 660 and like them, good bite with out having to worry about snapping the axle's as much. The at's should be good for all around work, but you can't do much better then a set of "factory like" tires for general use around the house IMO. I don't think I would go much bigger then 22's.
You can't go wrong with mud lites!! Not familiar with what the max size tire is for your hawkeye, but I would guess that you could do atleast 23, maybe even 24" before having to worry about rubbing, but I would check first. Bigger is always better, right?
I would also say go with bigger tires, but with the smaller engine I would stay smaller. You could put at least 25's on it, maybe bigger but they may rub, not sure. I wouldn't go bigger then 25's without a clutch kit and some other upgrades.