Your basic plan is fine. It will be slow driving all those screws. I prefer 1&1/4" construction staples. But screws actually hold better. It just takes forever, IMO. If your crawl space is damp, you need to locate the source of the moisture and eliminate it. Re-grade, re-direct downspouts, check for leaks, etc. And covering it ( the earth ) with a polyethylene plastic vapor retarder is called for and recommended. You should use 6 to 8 mil; .12 mil isn't even good enough for trash bags. You could lay a layer of 15 lb. or 30 lb. asphalt saturated felt over the OSB and UNDER the 3/8 plywood. Then use Fortifiber Aquabar "B" over the plywood underlayment. This will help considerably with the moisture vapor but not eliminate it. You could still have a moisture problem. That's why we suggest checking with a moisture meter. Then you know for sure. Putting plastic between layers of wood will accelerate dry rot of the subfloor as it will trap moisture in it.
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