Replacing a crawl space with concrete slab
You certainly wouldn't pour dozens of yards of concrete in there. You'd remove the organic soil, fill it with sand, and pour a 4" slab on that after setting up the plumbing. 

Alternatively, look at an internal drain tile loop, along with some ventilation. It would be fairly easy to trench in perforated and socked pipe inside the footing. The tough part would be getting through or under the footing.