I think a loose radiator cap will not allow the coolant to pressurize. The coolant's boiling point is raised when it's pressure is raised. With a loose cap, the pressure of the coolant is basically atmospheric pressure, and the boiling point would be lower - and some coolant could boil out of the system.
But if that were the case, I think it would boil out of the loose cap. That's where the hottest coolant exist. Well I suppose technically, the hottest coolant is on the cylinder head side of the thermostat. But from there, it goes to the radiator via the upper radiator hose. The coolant is "cooled" through the radiator from the top down.
If the radiator cap is on tight, and you have no other leaks (a BIG if right now), then the system is getting pressurized. If the system is getting too hot (as you have indicated), then it gets overpressurized. That is what the overflow tube is for. The expanding boiling overpressurized coolant gets pushed to the plastic reservoir until it is full, where it is pushed out the overflow tube, which is where I think you are seeing the leak.
Which brings me to 1 of 4 conclusions:
1. There is air in the system that can't get "burped" out. Air takes up volume. When the coolant is drained, or otherwise the system is opened up, after it is refilled, gravity may not allow the coolant to find every nook and crannie within the system (especially in the radiator and the engine). For myself, I always fill the coolant and start the bike with the cap off. I allow the bike to come up to running temperature and usually the water pump will move the coolant and force the air to "burp" to the highest point (just like when you burp the CO2 from your beer - at the highest point!! LOL). I top off the coolant, then put the radiator cap on, then re-start the bike and allow the system to pressurize and the fans to cycle one time on and off. Then check for leaks and top off the reservoir.
2. The fans are not working as they should. As previously stated, they should come on at 225 and go off at 215. Just because the are working in DIAG mode may not mean they are coming on when they should. If the fans don't come on until past 225, and/or they shut off above 215, then you are overheating the coolant, and overpressurizing it. You can check this in your driveway idling the bike.
3. The thermostat is hanging closed or partially closed. The thermostat for the bike is designed to open at a specific temperature to allow coolant to circulate. If it is hanging closed (or even partially closed), then the coolant in the motor can't circulate and will over heat because it can't get to the radiator.
4. The temperature sensor is not working properly. The coolant temperature sensor is screwed into the cylinder head and I believe it is just before the thermostat. If this sensor is faulty (or perhaps has a loose wire), then the ECU doesn't get feedback and the bike can overheat. I'm sure that might have something to do with the fans too.
I make these suggestions assuming there are no coolant system leaks, as you have eluded to so far in this thread.
I hope this helps.