Fair warning! I only know half of what I'm talking about. The the issue is I don't know which half. Increasing OM is a simple math calculation with a lot of complexities between the beginning and the end. Let's start with the sample. You send it in. The labs dries it if you haven't. Lets assume its 100% dry. Maybe it's different now. But a long time ago the OM content of your sample was determined by burning it. Lets say the soil used was one pound before the OM got burned out. It's much smaller but let's go with it. Now it weighs 15.75 ounces. What comes back on your soil results sheet? OM = 1-(15.75/16) = 1.6% in round numbers.
Fast forward back at the food plot. What do you need to do to raise OM 1-percentage-point...to get to 2.6%? Yes! Get more organic matter in the soil, but how much?
Let's say you took a sample of the top 6-inches just to establish a base from which to start. In this business we assume the top 6-inches weighs 2,000,000 lbs. So, to get that one-point boost you need to add 20,000 lbs of DRY organic matter (2,000,000 * 0.01). You had 32,000 lbs (2,000,000 *.0156) and added 20,000 lbs. Now you have 52,000 lbs of 'presumed' organic matter in you top six inches of soil or 2.6% OM ((32,000 + 20,000)/2,000,000).
It's not quite that easy. The conversion process is complicated by a number of factors. Nobody ever get's anything that easy. I'm not versed enough on the subject to go there.
What to plant, then, is the question. My reading tells me the root mass is more important in this than the vegetative mass produced, although both are contributors. My assumption is annuals producer more vegetation than root. Maybe 75:25. Perennials? I don't know - 50:50? Bottom line is to produce a lot of mass. And leave it alone.
Lets use sun hemp. I read it can produce up to 13-tons of dry matter although 2-3 tons is more typical. Cereal grains maybe two or three tons annually. And, the carbon content of each species is important. If one plant produces the same dry weight of biomass but different amounts of carbon pick the big one.
If a plant can rebound after mowing, it will continue to produce vegetative matter because it's aim is to flower, produce seed, and die. It just depends on where new growth originates.
Growing multiple crops in the same space in the same year (think double cropping) can produce an abundance of OM. So, too, does adding manure. Some types are high in OM so you get that in addition to what the crop(s) supply.
That's my simple minded understanding and explanation. It's a complex subject - like making a million dollars a year.