lift force from the tail and lift increases quadratically with airspeed
Correct
That means that the faster jet will have a turning moment 11 times stronger than the slower plane?
No, because the aerodynamic force depends also on how many degrees the control surface is deployed, more or less in a linear manner. That means that instead of deploying the control surface of say 11° as you do at low speed, you deploy it only 1° i.e. 11 times less in order to compensate for the 11 times higher speed's contribution.
Changes in altitude ($\rho$), comprimibility effects (Mach > 0.3) and structural deformations modify this simple linear relationship but the main idea still holds i.e. at higher speed you need lower deflections.