Pylonracr I disagree with your methodology. For maximum servo torque and resolution the closer to the center of the servo horn the better. Using the 5 degree arc of slop in the servo gear train example the linear movement of a connection point located closer to servo center will be less than the linear movement of a connection point farther out.
I once built a training aid using two protractors and bell crank mounted pointers attached to identical servos mixed to the elevator channel on my computer radio. One servo was set up with the shortest servo arm and the longest bell crank connection to give one inch of throw. The other was set up with the longest servo arm and the bell crank connection that also gave one inch of throw. All connections were made using ball links for slop free connections. Care to guess which set up gave the least amount of slop at the end of the pointer? Care to guess which one gave the most precise and smooth response to trim input?