Just happened to see this and thought that I would add...
The ground, regardless of whether it's covered or not (if the surrounding ground is saturated, do you think that the relatively dry earth beneath the structure would not wick that moisture ?) contains a lot of moisture and often-times, that moisture travels in one direction - up.
Concrete is in no way a vapor barrier.
Darkness and moisture = mold.
Clear, 10 mil plastic = bits of recycled plastic that has been re-heated/re-formed into a sheet that also is not an effective vapor barrier and degrades over a period of time.
I read your distaste for plastic, but I would not hesitate to possibly jack the dwelling up give you some working room, install a true vapor barrier (Stego 15 mil) that has been tested for vapor transmission, possibly add a venting system similar to a radon mitigation system and then install a frost apron around the structure, using environmentally unfriendly 4x8 sheets of two inch thick foam insulation - to direct rain water away from the structure.
I personally feel that your air quality could have an effect upon your health.
And...
if you are using natural gas or propane cooking appliances, rip them out immediately and replace with electric.
I apologize in-advance for advocating the use of plastic.
On my dwelling in Maine, which has a shallow, frost-protected slab on grade, I installed a Stego vapor barrier (to keep the slab dry and retard vapor transmission into the structure), a frost apron and applied a water-proof coating on the sides of the concrete (a dry slab = a warm slab) and the entire slab was poured on top of 2 inches of foam board insulation and I affixed the same 2 inch foam to the vertical sides of the slab.
The above processes were gleaned from university and Department of Energy standards for this type of slab and as well, I installed a radon mitigation system to be building code compliant, but never actually installed a fan or activated the system.
