The battery voltage is generally too high for a 370 motor, you need to use a 2 cell lipo (7.4v)
The actual voltage of a 2 cell lipo starts off at 8.4v and drops slowly to 6v as you use it up, so one of these will be fine.
I use a 2 cell lipo in my 380 powered piper cub, & flies great on it.

The motor in your flat out plane that you say is fine on the 3 cell 11.1v lipo, will be because the current draw will be much lower, by being driven through the 5:1 ratio gearbox to reduce the load, so this is why you can get away with it on that one.