Re: Any reason I couldn't put bigger tires on X340?
I agree that you may be better served with changing to a more aggressive tires rather than upsizing it. Larger tires lowers the overall gear ratio, it increases speed but reduces torque. It increases stress on the hydro, and makes your brake less effective. You mention about going up a slope, not knowing how steep it is, your tractor will actually has less torque to tackle the hill even if you get better traction. I would not want to chance it with a K58. You weakest link is not your engine, but your hydro.
For the mower deck, you will need to re-level it as front vs. rear now has a half inch difference. You will also need to drop mowing height by 1 inch as your tractor is now a inch higher off the ground in the back, and 0.5 inch higher in the front.
Personally, lawn tractor is form follows function, I would not sacrifice durability and performance for look.