As far as moving from theory into actual practice, I'm just guessing, but here's my guess. A lot would depend on how severe the constriction looked. If it were my tree and I exposed a root tightly wrapped around and partially embedded in the main stem, I would cut it ever-so-carefully to minimize additional damage to the already-damaged stem. This could be tricky, because part of the root you're trying to cut will be sunk into the main stem, below the surface, so you won't be able to get at it with loppers or pruners. I would probably work at it with a small wood chisel, taking little "bites" and going very slowly as you approach the buried cambium pressed into the main stem. Once it's actually severed, I'd try to carefully pry the rest of the root out of the "groove" so the main stem will have room to fill in again over time.

Again, this is all guesswork and may well not be the problem at all, but if it is, and the encircling root is large enough, you'll have to assess how much impact it's removal will have on the tree, in term of the water it's providing. On the other hand, since you've already thinned the canopy and there's not much foliage anyway, maybe you won't have to worry about additional water loss through the foliage. Anyway, now I'm really curious to find out what the real problem is, so please keep us posted (maybe it'll turn out to be a big bunch of beetle grubs or a gopher with a taste for latex)! Pictures would be nice, too, if it's something that's clearly visible. Good luck!

Once the problem is identified, so can a solution.

For RKN to affect a tree of your age/size, the infestation would need to be pretty substantial and evident.  If the you see evidence of RKN, carefully put the dirt you dig back into the hole.  In order to save the tree, you will want to air-layer the top.  Try your best not to move dirt to other areas of the yard on your clothes, shoes, tools, etc.

If you see evidence of a root girdling the trunk of the tree, cut the root where you are digging.  Use a pry-bar, chisel, knife, etc. to move the root as best as you can away from the trunk.  Do your best not to damage the trunk with the saw or pry-bar.  Since you can't completely dig up the tree (yet), cut out as much of the offending root as you can access in the hole you have dug.  The rest can be removed when the tree goes dormant.

Also, check the area around the trunk for compacted soil/growing mix from when it was in the container.  Push a garden stake, chopstick, screwdriver, etc. into the dirt underneath the tree.  If you meet with a lot of resistance, it could indicate the compaction of dirt causing girdling.  Try to loosen the soil with whatever tool you're using to poke with.  Don't worry too much about moving or breaking a couple of roots.

The second two issues are not uncommon problems with container grown trees.  If you imagine your tree in a 1-2 gallon nursery container, the evidence should be in that zone.

So I dug around the trunk and found that the roots are not wrapped around it.  There are no balls on the roots, they seem healthy. One thing I noticed is that the soil is sandy, and it was very moist.  I had a weed preventer that was covered with woodchips, which was keeping the moisture in. I ended up taking it out and got some fine soil that has nutrients and it says that is formulated for trees and shrubs.  I also mixed in some cow manure.  I am also working on rigging up a canopy for it so that it has shade so that the bark doesn’t burn from the sun.  I am out of ideas of what it could be, the only thing I am thinking is that since it had so much fruit on it last year that it wore its self out. 

Absolutelly true ,you got it.