Peel them top-down from the midline of the back down to the elbow/knee. Ring around the pelvis and above the knee, plunge to the femur, peel around the femur, done. Knuckle @ the elbow up front, peel off the front. Grab the up-side strap. Done with one side. Flop over, repeat. Dive in for the tenderloins last.
No more hair on the meat than the standard gut/hang/skin while hanging and no blood on the garage floor @ home.
I'm not a believer in "Quick cool = tough meat". I believe in "As cold as you can (without freezing) as quick as you can."
I can do a lot of things at home to make things more tender. Slow down the cooking, add acid to the cooking process with tomatoes/tomato juice/paste. If really tough, ketchup and cola in a crock pot all day. Less acid longer would be an overnight soak in olive oil, some mild heat on the BGE with the diffuser in place and a pan of apple juice on top of the diffuser to keep things moist and caramelize the crust just a little, spend ~2hrs getting to ~130ish, pull, cover w/foil for 10min, slice and enjoy the "melt in your mouth" goodness.