Tony & I use pretty much the same method of settling the grounds in campfire coffee, but I do it just a little differently, just as you'd expect.

I try to stir my grounds down, right before the pot comes to a full boil. I use one of those blue/white speckled enamel coffee pots....around 8 cups of coffee, as I recall. If I forget to stir it down before the full-boil point, a 'cap' forms on the top that the bubbles will not penetrate....that cap gets pushed up and past the strainer holes and sometimes up & over the top of the pot....even with the lid in place. That's a real mess, especially if your source of heat is your old Coleman 2-burner and one that can be avoided just by keeping a close eye on it....a full rolling boil is not necessary and, if truth be told, makes a better cup of brew when you stir it down and avoid a full boil. After stirring it down, I pour a partial cup of cold water down the spout to clean it out and the rest of it goes into the opened pot. At that point, I take it off the heat and set it at the edge of the campfire to steep for a few minutes. Right before I pour the first cup, I grab the pot by the bail and swing it like a pendulum 2-3 times to build up some inertia and then swing it over my head in a full circle 3-4 times.....check first for low hanging, overhead branches!

That last step really puts the grounds where they need to be.....at the bottom of the pot.
Works for me.
