Just by the way, we used to save left over mashed potatoes and press them into patties for frying. They're pretty good that way.
Most of the time spent on mashers is peeling the potatoes. Do that ahead of time, even the night before, keeping them submerged in cold water. Then make the potatoes just before you pull the turkey out of the oven. Mash them while the bird is resting. Make sure and use lots of butter and a little heated milk.
Aha, so the egg is the secret!
... what I'm trying to avoid-- the last minute cooking and mashing and stove mess!