Batteries require 1900-2200 milliamp charge (acording to my tp610c). This seems to verify that the batteries are depleated after a flight of 2 mins. thanx Bart
I think that's your proof that your heli is fighting some serious friction/binding.
The excessive positive pitch, +15 degrees, is definately a drain on the motor, ESC and batteries. Fixing that will make a big difference.
Loosening up that belt will definately help as well. Loose is good as long as it doesn't slip.
In addition to checking the main gear/pinion mesh also check all of your ball links. Any binding there will cause the servos to overwork and ESC to heat up.
Sounds like you're making some good progress.