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.

The run 4 vaporizers filled with bleach for a week or 2 to kill anything that might have spawned down there, then dry it out again.

During the inspection, a look under the homes showed some failed vapor barrier's.  

I would get a roll of batt insulation with no paper backing (vapor barrier) and lay on top of the insulation in this area. 

Another concern, if you have an open sump liner(bucket) or one with gaping holes which allows you to see the water inside keep in mind that this accumulation of water is emitting vapor into the surrounding air.

Steel beams, and vapor barriers have been installed but the inspector said it is just a Band-Aid.

Unless a good vapor barrier was installed below the concrete slab (rarely done correction in residential construction today and never 10 years ago) moisture vapor will migrate through concrete.

btw: sand would absorb any residual contents and when filled to the top of the tank, evacuated all volatle vapors of any concerns.

Assurances, promises, and words are like vapor... if a person decides to do nothing later on, there is no way to force any partner to physically perform.

@Holly Scott why do you think a vapor barrier is needed?