Is this house on a slab?
Is it possible that the plastic pipe used in the sewer system is broken, allowing moisure to wick itself up through the slab? Slabs are supposed to have vapor barriers but have holes all in them from pipes, tears, seams, etc. Conventional foundations allow for a visual inspection.
The photos I looked at seem to imply a constant source of water. It does not rain down there 365 days per year and drier weather tends to make the mold less. So the mold should come and go to some extent. This makes me wonder if the issue is vapor barrier related or not. Hard to diagnose with relatively little information related to the locations, relationship of the mold " hot spots" to the exterior walls, plumbing, etc.
The sewer pipes can be video taped by any number of plumbers for a relatively modest fee. You can easily see faults in most of the system.
BTW, newer construction codes in many areas require that the sewer pipes be supported by the slab using stainless steel hanger so that if the soil under the slab sinks differentially, the pipes will be supported by the slab and do not move relative to the slab. This differential movement is what breaks the pipes (unless they were damaged during construction). Sewer systems in most code areas are required to be smoke tested before the slab is poured but not after. Slab pouring can be brutal on the underground pipes, with insipient faults that may not manifest themselves for years. These faults can come from rising/falling water tables, roots, etc.
I know that you have spent a ton of money on this thing and don't relish the thought of more, but a really good registered professional mechanical engineer might be of some value.
PS: The duct board ducts are notorious for leaking cold wet air. If they leak enough, that could also be a source for the the moisture to fed the mold. FYI, the best system is NO internally insluated suct, use metal duct and seal ALL joints using duct mastic. Duct tape does NOT hold up, I don't care what the installer says. Is this more expensive? Of course, but in a bid situation with good contract documents, 3% of the HVAC cost.