Panaracer Paselas are everywhere, and are a really nice tire that comes up to at least 35, though they run a little small so it's more like a 32. The Forte tires from performance are basically the same thing, and they run small as well.
The karate monkey can probably take just about anything, but I would shoot for a 35 and run it at like 75 psi. This will be a whole new world compared to a 28 at 110 or whatever. It is going to feel a little slower, but TANSTAAFL. If you want you could go with higher pressure in the back since it's the front that's killing you. Hell, you could even put the big tire only on the front, people always think this is going to be goofy but like many things you never notice it unless you're trying to. But get bigger than about 35 and unless you weigh like 250 you're just dragging around extra tire without getting the benefits.