Just went through something very similar to this. The thread on that is
here, but the summary version is this:
When we bought the KJ, it had multiple cooling system issues that took months to completely figure out. A lot of this came down to changes in the seasons showing up different weaknesses, but it had a dead fan clutch, dead thermostat (I'll highly recommend the HDS Model 001 if you can stretch to it), dubious-at-best radiator, and radiator hoses that looked OK on the outside but that could have been collapsing under motion.
Each item was changed at different times: fan clutch first, then the thermostat in Winter (driving in 9°F weather with no heat really sucked), then the fan clutch again (multiple times, along with an upgrade to a GM heavy-duty fan clutch and 11-blade fan), then finally the radiator and hoses. This process started at around 112,000 miles and finished up at 120,000.
The reason I mention this is that you may be looking at a multi-layered problem. From the descriptions you're giving, the fan clutch is likely a goner, so start there. Move on the thermostat next, then the radiator and hoses. I'm picking these in ascending order of cost, but modify as necessary if something obviously wrong crops up.
Good luck - hopefully yours isn't in as dire need of everything as ours was.