I would prefer to replace the whole sector / pitman shaft. The
other possible way to remove the backlash when all else fails is to machine out the hole which the eccentric bolt fits into, and machine a slightly bigger eccentric , to get more adjustment. You have to be careful though ,because tight in the centre of the sector gear that is worn, may be too tight on full turns and lock and jamb.
Maybe a combination of regrind the Sector gear , and remachine the adjusting eccentric is the way that the Sydney company does it.
If it was repaired , I would want it done by someone who does it ALL THE TIME.