We had a Class C that was pretty much similar. 1983 E350 chassis with the 460. Running hot was never an actual problem, but it'd clutch the fan in pretty often. It had aftermarket A/C (so-called "Dealer Air") so the configuration was probably different. Still it had Radiator, Condenser, Trans Cooler, Oil Cooler, Steering Cooler, all up there.
OP did the right thing, flushing the radiator FIRST. Simple inexpensive things first, like new thermostat next. If a 'stat gets overheated it can lose its ability to fully open next time.
Also, MAKE SURE all the shrouding and baffles are in place. The Fan needs to be proper depth in its shroud and any little rubber/plastic/metal seals/deflectors need to be there. In other words, you want all the cooling air to be pulled through the radiator and cores to get to the fan. Not pulled from elsewhere and bypassing those parts.
That FORD OEM Fan Clutch was a simply stellar component. It'd idle quietly till needed and clutch in HARD. First time it did it on the interstate I looked in the mirror for a biker gang passing us. We had hit a grade! I looked at the gauge and it was above normal. Topped the grade, temp dropped, roar smoothly decreased and went back to normal.
Our fan clutch was working after 25 years and over 100,000 miles. I mention all this because it seems the OEM is long discontinued and many who have replaced theirs with aftermarket brands have not been satisfied. Be VERY sure yours is bad before you replace it.