Pam, Perhaps you can check around and see if it is possible to blow insulation into the crawl space. All it would take is cutting one or a few small holes in the subfloor for the contractor to insert a tube for blowing the insulation. Because the crawl space is so shallow, it may not take that much insulation.
First let me say that I have never heard of anyone doing this. One of the biggest concerns will be the effect of moisture on the insulation because it will be in contact with the ground. Certainly you could not use cellulose and I doubt if fiberglass would be suitable. The insulation should also be bug and mildew resistant.
If there is a blown styrofoam or other closed cell insulation then it would be the best as it absorbs little or no water.
What do others think about this approach? Will it work?