I looked into crawl space moisture barrier systems in the net. The standard seems to be 20 mil plastic sheeting, doublestick tape and/or polyurethane caulk and plastic fasteners into holes drilled into the concrete foundation. This is all straightforward and common sense stuff. I am guessing that 6 mil plastic sheeting will do the trick just as well as the 20 mil stuff as long as no holes are poked in it. The only thing I am not sure of is whether the doublestick tape used in these systems, and regular polyurethane caulk, will stick to the 6 mil plastic available at any lumber yard or home improvement center as well as it sticks to the 20 mil plastic used in the various systems, or if the 20 mil stuff is made of plastic that is better in this regard.
Another thing that I am wondering about is whether it would not be just as well to apply 6 mil plastic to the bottom of the joists and seal the edges against the top plates of the underpinning. Once the moisture that gets sealed into the joist bays evaporates out through the floor and into the house, it seems to me that the sealed joist bays should remain stable as far as moisture content is concerned. The advantage to this method is that on days when relative humidity is very high, a crawl space will still be moist even with a vapor barrier on the ground.