I try to plan an easy breakfast and lunch, say, oatmeal in the Jet Boil, lunch of lunchmeat sandwiches and chips.
Dinner, when the day is done, I try to get a bit fancier. Usually some kind of meat is involved, and some kind of vegetable on the side.
I try to design all meals to leave as little waste as possible. I don't use disposable plates or utensils. Durning lunch, a paper towel serves as a plate.
During supper, what dishes are dirtied in the cooking and eating process, we take the time to clean. As early as we often settle for the night, it isn't like there is a rush. Taking a little more time for a properly prepared and tasty meal always seems worth it.
As for cleaning, the pots and pans usually are given a little water, then put back on the burner and brought to a boil or close to, and that often loosens everything up enough that a light scrubbing gets them clean. The plates and utensils, I don't have a sink, but I will usually heat some water in the biggest pan I have, and use it as a sink to clean the plates, then clean it out.
For me, I consider the extra hassle of cleaning dishes worth it for the better meal, and the lower trash impact.
What little waste that is left over is either dumped at the next fuel stop, or if it is safe to burn (paper towels, some food scraps) it will hit the fire.
I don't like having to haul trash around, so I try to plan where minimal trash will be left over, so what I do have to haul is compact and hopefully not offensive to the nose.
This system has worked pretty well so far.
On the subject of fire rings, we are not prohibited from having fires or constructiong fire rings (unless fire risk is high, which is usually well publicized) in the two NF's in Arkansas, but we are encouraged to seek primitive sites where one already exists when possible.]
I always like having a fire when camping. It is part of the charm. I won't go so far as to say I would stop camping if prohibited, but it would be a bummer. Fire rings don't bother me, personally. Most around here are constructed of native rocks, and it would take all of 10 minutes, a shovel and some rock moving to all but erase any sign a fire ring ever existed. There are a lot of worse things in my book, like litter, wildcat trails, and trails closed because of abuse by irresponsible ORV'ers.