"Compaction" is caused by tillage and/or traffic across a field. If it is in native grass, and has been for a while, there shouldn't be any compaction there. It may be that particular soil type is just very compact by nature. If that's the case, it may not be suitable for tillage.

I have a subsoiler that I use every now and then, but the purpose of it is to remove the compaction caused by combine, grain cart, tractor, plow, and drill traffic. The goal is to go 1" below the hard pan. Any more, and I am wasting time and wasting money. A tiller will generally only go the depth of the tines. Go deeper than that, and you'll start wearing on the carrier bearings. Most farming practices that use a chisel or a disk will generally also focus on the top 6-8" soil. The goal is to loosen the soil enough water and roots can penetrate.

Whatever the organic matter is in your soil with grass on it now, it will decrease if you start tillage. And as long as tillage continues, you will never be able to effectively add organic matter to meet or exceed what it is now. Tillage aerates the soil and resizes the organic matter. With larger surface to volume ratios and more air infiltrating the soil, organic matter decomposes much more quickly.

My first suggestion is contact your local extension agent or NRCS conservationist and see if they have any advice. You may very well have some valuable native plant species on your acreage, and you might be better off trying to manage and help propagate some of the native species than trying to convert the native cover into cropland for a food plot. Or maybe a portion and leave a portion. They might also be able to give you good advice on what you can grow in your area.

If you do choose to grow some type of crop, your organic matter and your soil health will be better if you reduce tillage as much as possible and practice conservation tillage as much as possible. Try to keep the surface covered as much as possible, either with something growing, or with stubble. A soil test is never a bad idea. Something as simple as just not having a very small amount of one micronutrient may mean productivity is cut in half.