I would suggest a "hardpack" tire with a tread like the Maxis Tread Lite. It has minimal center tread but side knobs that aid in corner traction. Other tires in this class are the Panaracer Comet, the Kenda Small Block 8 or the Forte' Dartmoor. I haven't had direct experience with the Panaracer or Kenda, although I've used other tires in those lines and found them to be excellent products. I have a couple of bikes that are equipped with the Dartmoor and they are an excellent tire for mild off-roading. They don't do really well on loose trails but the excel at hardpack. And they are cheap...around $18.

Honestly, you don't need rims as wide as you have. You don't really gain much from having rims that are an inch wide, which is really ooooold school. You are carrying around a lot of excess weight for no real gains.

That said, you shouldn't have problems with higher pressures. But then you shouldn't have a problems with any rim. 80 psi might be a bit high, especially if you are riding on unpaved or unimproved roads and trails but I regularly run 60 to 70 psi on 2" tires using rims that are around 17mm wide without problems.