You might not be able to pull this off because of space, but I have a few compost piles. One is the short term and it's basically
wood chips with kitchen waste and
coffee grinds. I flip it a lot and it's pretty active with a lot of pockets of black material. Smells earthy, the whole bit.
There's also my very long term one. Dog shit, dead rats, and all that nonsense goes into there. I throw in
enough wood chips to keep the balance right, and have only ever added to it over the years, never used any of the material. I don't know what I'll do with that pile. My guess is that I'll start a second one, stop using the first one, and in ~10 years the first one will be fully deconstructed that I can use it for some
trees.
You can also vermicompost dog poop pretty effectively. I had to shut my worm bin down for other reasons (a bear tore it apart), but I tossed some dog poop in there and the worms destroyed it. Worms are voracious consumers.