The floor is actually 3/4/6's and it's not over a crawl space. This is sounding like moisture content in subfloor is the issue? We will have someone check it out from underneath.

the floor was improperly fastened and most likely installed into wet subfloors,however the latter would be more evident with cupping in the flooring.

was the subfloor OSB or an actual plywood?

the shoe wasn't nailed properly either as the floor is still laying down and the molding went up.

cracking and popping like that is lack of fastener hold end of story..high moistures would heavy cupping and/or actual buckling.

it would be interesting to know what the supposed moisture readings were that they presented to you