KISA, your idea of using a 'modified', (to give full rotation), servo will not work, as they rely on the 'feedback' from the 'feedback' pot, which is driven off the gearbox assy. If you file/cut the mechanical stops off in the gearbox, the centre wiper arm inside the 'feedback' pot will be destroyed/damaged.
Sorry, but your original idea is best. Maybe try my idea of the drive belt onto the focuser knob. I use 'O' rings, (from a Bearing Supplier), as they are very cheap & reliable. Not much stretch at all.
HTH.
L.