Concrete will not stop humidity. Some heavy plastic sheet covering the crawl space may be a good idea.
Also, how about adding some ventilation to the crawl space. I doubt that closing the vents was a good idea, despite the rain outside. Let that insulation dry out. Also, you should have put a vapor barrier above the crawl space bats to keep inside humidity from. Maybe your bats had a built-in vapor barrier on top. Maybe your flooring above serves as a vapor barrier.