I had a similar experience, so take from it what you will...
Buddy had a nice older Concourse that wouldn't stay cool.
"Bring it over!", I said with confidence. "It's probably the thermostat. No biggie"
That bike was in my garage for 6 months.
3 thermostats, 2 radiators, 2 full flushes, still having issues.
(with pulling and reinstalling the damn carbs and intake boots between every damn fix got REAL OLD REAL FAST)
Finally I'm convinced that it's the water jacket itself that is clogged and full of crap, so I get some Muratic Acid and slowly flush a bunch of CRUD out of the water jacket!
AFter that, it ran like a top and lived all day in the lower third of the gauge.
My theory is that somewhere along the line P.O. put stop leak in it and then topped it off with well water or some such.
The acid attacked the calcium deposits much faster than aluminum, so by being careful and not letting the acid sit in there for long periods we got some seriously gravel sized chunks of calcified crap to blow out of the water jacket.
Good Luck!