I am going to go out on a limb and suggest something completely different.
Start near the center of the arc where you are certain that you are tracking perfectly and re-check the centering on your LNBF, as well as the focal distance--for maximum signal and minimum sidelobes. All of this is extremely important because you are using an extra large 12-foot dish.
The larger the dish, the more physical forces you are fighting with not only in actually finding the perfect mechanical alignment of feed devices, but in backlash from the weight of the dish itself and the physics of counting. As you cross due south there will be a substantial shifting of weight, as you are pushing Up, then starting to drop over the center of gravity. If there is any play whatsoever in the motor drive linkage or counting, positioning may appear to be less than accurate. However, if you are consistently starting on one end of the arc, going to the other, and then coming back to the original start point and the dish position numbers are not changing in the end, you may not have a counting problem with the positioner control, but rather are just dealing with the physics of having a monster dish. There will be sidelobes, and you can be fooled, especially on C-band, where the hottest signal is. This will be most noticable if you do not have perfect centering and distance on your LNBF. Try aligning a 16 foot dish and it gets even worse. A 12-foot dish is just simply a lot bigger technical challenge to align perfectly than a smaller 7.5 or 10 foot reflector, and you must be a perfectionist in its initial setup.