Good luck with that.
Have you thoroughly checked the worm and gear for the exact cause of the problem? Is the worm shaft straight?
I suspect the fact of the matter is that to attain the low backlash that the Haas tables generally exhibit requires a great deal of care in cutting the gear, as a much closer tolerance is required than for a commercial gear reducer. Concentricity of the spindle and gear assembly is critical as well. Alignment of the worm and gear is critical.
Is the shop you are hiring going to be able to fiddle and fuss with this gear until they hit the magic numbers?