With insulation between the floors joists, and essentially an open crawlspace (where air gets in most of the year), then what you have is the floor joists themselves becoming colder than the actual flooring above.
Once the floor joists becomes colder, condensation from the outside air turns into moisture on them, they become wet and eventually turn black and rot...over time, not next week!:laughing:
That's the big picture; however humidity i.e. vapour in the air can come from two places in an open crawlspace: the air, like I just said and the soil below. Ideally, you should be trying to reduce, as much as possible, the evaporation of humidity from everywhere - including the soil - and that's the reason people put a Level 1 vapour barrier (6 mil poly) on the soil. Some people even tape the seams together and tape the plastic to the crawlspace walls, by about 4-6".
So tell me are the bottoms of your joists, damp or wet at all? I don't see many crawlspaces up here - but there are some still in the older houses built in the 20's and 30's. Problems occur in these homes when a non-breathing flooring material such as vinyl rolls was put down in the 50's and 60's...then came the idea of insulating down there between the joists to warm the floor. Nowadays, we have even greater problems...
Nowadays, the concept of an "open" crawlspace makes little sense. Now we condition them like the rest of the house, i.e bring the crawlspace into the building envelope.
So, IMO, I'd cover the remaining half of your floor and tape the pieces together. Then, I'd look into doing something to warm up those floor joists I mentioned. I'd also look into increasing the square-footage of open ventilation access vents you have now with a view to making it as effective as possible.