My dad was a butcher as well. I've only cleaned 25-30 deer and haven't had any problems with the meat. He taught me using a saw and then we switched to boning the meat out long enough ago that I forgot how to steak & cut one up with the bones in.
Perhaps a reason for the lack of my having any encounters with the glands is that we cut the legs off above the hocks and tarsal area - there's no meat there, so it gets cut off.
Another reason could be that I skin from the head down - not from the legs down. That may be another difference. The guys down here use gimbels and I use the antlers.
I think it goes faster and gets less hair on the meat.