First, I'm a builder with thirty years experience and I have built new homes in many climates. Next, you're correct, a lot of posters here respond with what they know to be correct in their specific region, and it has nothing to do with yours. Finally, the whole " everybody is a building inspector" situation gets a bit old. There are plenty of jurisdictions that have rules like the ones covering your case, or like most in my area, have no interest in what you do to remodel, or repair existing structure.
Now, on to the situation you face. As you correctly note, there are hundreds of thousands of uninsulated, vented crawl spaces in your state, and they obviously function, as many are supporting homes that are a hundred years old. Obviously, they are not optimal, since the vast majority of new construction takes place on concrete slabs, avoiding crawls. Your board sheathing is solid enough to build up, but not treated lumber. It may be one of the older southern pines that can be pretty rot resistant. In your situation, I would first re-nail, or screw all the boards to the joists. This may be a bit of a challenge, as old wood can be amazingly hard. You may find success with 2-1/2" deck screws, or #10 common nails. It may be so hard that only a nail gun will do the job. Next, you need to find a floor sheathing product by Huber lumber, it's called Advantech. It looks like OSB (chip board) but it is about the most water resistant stuff out there. It's heavy, hard on saw blades, and about as expensive as regular plywood. It comes with a fifty year structural guarantee, and it does not swell or delaminate. You probably won't have much luck landing the edges on floor joists, since many older buildings were not framed on exact 16" centers. I would install it with an air nailer, using 8D ring shank nails designed for installing subfloors. If you want to do a really solid job, you could use a belt sander, or floor sander, with a very aggressive belt, and grind the original boards clean. You could then both nail and use subfloor adhesive to bond the Advantech to the old board subfloor. Advantech is a single ply subfloor, you can patch the joints and nail holes, and use the tiles you mentioned. Additional vapor barriers, used with an OSB or Advantech subflooring, might lead to rot, as the material is impermeable, and in effect it's own vapor barrier. You never want multiple vapor barriers in a situation like this.