You misunderstand Gyroscopic Precession. It's not a constant turning force, it's a reaction to a change in orientation. The "d" in the diagram is delta for change. The amount you change one axis affects the change in the other axis.
When you change pitch GP reacts with yaw, when you change yaw GP reacts with pitch. Precession to the right would only result while pitching up. Pitching down would result in precession to the left. Level sustained turns are relatively steady in pitch so GP is not a factor, vertical turns are not, this is why loops are so much fun with the rotaries.
There is no way the Camel can have a higher sustained turn rate due to GP. Sustained turn rate is simply thrust, lift, and drag.
It's true that if you are slow in a rotary engine fighter like the Camel a 270 degree descending turn can be faster than a 90 degree climbing turn.
But, if you start slow enough in any fighter the climbing turn will be slower than a descending turn. With a rotary engine like the Camel or Dr1, in a slow climbing turn, you can lose enough stability that you rotate on the yaw axis, reducing your lift enough to drop you straight down. So it's clear why pilots would avoid a right turn. It's a better turn left than right, but it's not higher sustained turn rate.