Bill - what does the dealer that fixed the T/B issue say? Are they on record as being notified that you believe the T/B repair has somehow caused your intermittent overheating? Have they encouraged you to continue to ride the bike, or did you make a decision to do so on your own?
Stay with me for a min...
Do you have any written records associated with your return to the dealer, and any explanation given therein? Has the dealer run a pressure test on the cooling system (connect a hand pump with a fitting that fits in place of the radiator cap, then pressurize the cooling system to Yamaha's specification, thereby simulating the pressure of the coolant during a high heat condition)? If so, were any leaks detected? Have they verified that the fans cycle at the temperatures Yamaha specifies?
At this point, it's clear that you are unable to pinpoint why this condition is occurring. And the forum, despite its very best efforts, hasn't been able to help much either. At issue here is "who" is responsible. If it's a $40.00 fix, it doesn't matter. If $4,000.00 - big problem.
If it were my bike, at this point, I would do one of two things:
1. Start taking it apart myself and investigate. I'd pull the tank and get down to where the T/B could be fixed. I'd examine the entire cooling system (eyes on) and verify all hoses routed correctly and tight. I'd then pressurize the cooling system and look over every mm of it to verify not one smidge of coolant leaking. Then, with the tank raised, I'd start the bike and let it idle until the overheating starts and see what is happening. If you are smelling coolant then, you should be able to see it. If the fans at least come on at the 225-ish temp, then we know that part is right. We can't rule out a partially closed (or malfunctioning) thermostat with any of these test. The only way to do that would be to pull the T/S, and with a thermometer, test it on top the stove.
or
2. I'd bring it back to the dealer and say "fix it and don't call me until you do". Whatever is causing the problem is real. Something is not right. When they find out what that is, either it is related to the T/B repair or it is not. Based on the marked differences between these engine systems (cooling system v/s Fuel Mgmt system), there should be no doubt as to the root cause of the issue. When that is determined, if related to the T/B, I'm sure the dealer will make it right. If by some major coincidence it is not related to the T/B repair, then at the very least you will know it is fixed. Pay the man his money and take satisfaction in your resolve.
I don't think running the FJR at 250 degrees for a very short time is going to be detrimental to the motor. However, I don't know that. Running a motorcycle with a known history of overheating problems is kind of playing with fire. If you damage the motor, regardless of the root cause or how you got there, the resolve is going to be VERY complicated. The dealer is not going to roll over and give you a $4,000.00 motor. Even though the most grenaded motor can be fixed, but the fall out from that can also be lengthy and complicated (and very expensive).
How does this logic sit with you?