I "blued up" the gear in a gear box. I used the same gear box (and shafts, worm, bearings, etc) with an older gear that we had from the previous vendor. The older gear ran quiet and the dye was taken off across more of the tooth.
Our gear box has to run in both directions although the load is typically in one direction only. If everything were to print and at the nominal dimensions, the gear would run .006 offset from the worm centerline. I'm not sure why this was done (this was designed 40 years ago and has been working o.k.). Maybe it was to get the oil in as you said.
I talked to the vendor and he doesn't think it's probable that 1 or 2 gears in 10 would be off. He reminded me that we had talked and decided that we had agreed to decrease the backlash of the gear set by a few thousands. Maybe that has something to do with the problem. I asked him what was involved in setting up the hobber and he said they set the machine, run a gear, inspect it, make adjustments and then run the whole lot. He made it sound like there were two adjustments on the hobber - one to get the teeth centered on the width of the blank and the other an angular adjustment. Is that typical of hobbers (that there is an angular degree of freedom)?