OK, after re-reading your post..."(only 2amp supplied there.)" you obviously meant only two amp draw is EXPECTED at the tail. My assumption, my bad.

But then the question is.. is that 2 amps max, or avg.? Big difference. I've never had to measure or test it.

Well I hope your right about the required value because if the fuse blows in flight you won't be worrying about the fuse for a while.

Is there something binding the motor? With a V3 there is no gear, it's direct drive unless you've converted it or something.

Is the tail rotor rubbing against the motor housing or mount somehow causing increased friction or drag? This would cause current draw problems.

My advice is based on the fact that there are three components involved here, the tail ESC portion of the 3 in 1, the wires to the motor, and the motor.
Have I missed something?

If you've replaced or verified all three, I'm at a loss here.