I have a slightly different method that's worked well on the few dozen skulls I've done. Most of this info, but not all of this, has come from my taxidermist.
A rolling boil is fine, but make it a LIGHT roll. Just on the line between no roll and a slight roll. It will make the process go faster but you need to pay attention to it and not over cook it or it will fall apart. There's no need to spend many hours simmering it, just pay attention to how done it's getting.
I think I've done 1 or 2 outside but the rest have all been done on the kitchen stove with the range hood fan going, which is used mostly to vent the moisture. I (and more importantly, MY WIFE) have no issue with any "smell". Hey, every Thanksgiving we boil the turkey carcass for soup broth. Why should a fresh deer skull be treated any different?
I skin the head, remove as much meat as possible, take the eyeballs out, remove the jaw, stick the skull in a metal bucket with water, Dawn dish detergent and Arm and Hammer Super Washing Soda (or borax). It boils the skull clean enough to power wash it in a little over an hour.
Put on some rubber rain gear and power wash it (rain gear, rubber apron, rubber boots, etc because power washing is messy). Nothing cleans out the brain cavity and all the tiny little nooks and crannies, ducts and ports like a power washer.
I like it clean but not snow white. I seldom whiten the skull. I like the natural, ivory color. Very rarely, I will give it a quick dip in DILUTED bleach for a few minutes then rinse well. I've not had the bone deterioration that some guys claim bleach causes. Maybe it's because I don't bleach full strength and I rinse it.
I usually write with a pencil, details about the deer on the underside. Where taken, year, antler score, stand name, etc.
Your kids or grandkids will like to see some details about the critter. A bare skull with no info on it is a lot less interesting.