Also, there was no insulation or vapor barrier under the house - electric bill was $800 for December/January.

There is usually a vapor barrier on the dricore, etc.

Another solution I have read is to install a vapor barrier.  

This deal was pretty much turnkey other than needing a new vapor barrier (estimate for $500) which I plan on doing myself.

We've brought in two dehumidifiers which are helping, but I'm not sure what the root problem is or even who to ask for help.One contractor said moisture is coming through a hole in the exterior stucco, but another said no way because the vapor barrier would block it. 1st one recommended installing insulation, but I've also read this can increase condensation problems.

Wood would be a bit cheaper but it should have a vapor barrier over it before the stucco is applied, unlike block.If you ever need to run additional wires, cables, plumbing, etc., it's nice to have wood walls rather than block.There are plenty of wood frame homes down here.  

Then lay you're vapor barrier on top of that, followed by the floor covering itself. 

Wear a respirator with organic vapor cartridges as you apply it.

Carpet/pad/install for me is about $3.50/ft with rem pack carpet, but I get high end pad with vapor barrier for my rentals. 

Starting with the slab, it does not usually have a vapor barrier or the correct PSI concrete.