Letting moist/humid air into your crawlspace in the first place puts you at a disadvantage. Current thinking is that it's much better to seal and insulate the perimeter of your crawlspace, keeping that air out in the first place. It's known as encapsulation, and can easily be DIY'able in many cases.
There are two basic components:
1) Thick, sheet plastic vapor barrier across the floor with taped seams. This prevents soil gas and moisture from entering your crawlspace through the soil underneath your house. 6 mil vapor barrier can be found in a bunch of different sizes at any home store for less than $0.10/sqft.
2) Rigid foam panels along the exterior to air seal and insulate. Ideally, you'd do the whole crawlspace wall, but that might blow your budget. The most critical parts are sealing up the vents, and the joist bays which are currently uninsulated. These areas above grade will have the most heat transfer and therefore most bang for your buck. 2" thick XPS rigid foam board is ~ $40/sheet. If your joist bays are roughly 10" tall x 16" wide, you'd get 27 small filler panels out of a big sheet (1 per joist bay).
*You may need a dehumidifier as well, or a way to utilize any ducting in the crawlspace to help keep that area from getting too humid/musty once it's more sealed up.
The idea of venting crawl space air into the house, no matter how much I've cleaned it up, simply does not appeal. I suppose if you get rats you'd know it from the smell?
You're already doing this right now though. The stack effect brings things from the crawlspace into your home no matter what. Especially if there's any ductwork or other penetrations between your living space above and the crawlspace below. Subflooring has joints that aren't sealed. Dust, soil gases, mold, humidity, musty smells, etc are exchanged between the two spaces. That fungal growth you're seeing in the crawlspace is likely present in your living area to some degree.
Crawlspaces tend to stay relatively temperate compared to outdoor air temps. It's not like your crawlspace is 30F while your living space right above it is 70F. It's common to run exposed copper plumbing through vented crawlspaces in places that go weeks or months at a time below freezing, and these pipes rarely burst because the temp in the crawlspace rarely gets low enough to cause any damage if the space above is conditioned. The crawlspace's moderate temps are not only due to conduction through your floors. Convection plays a big part of it. By properly sealing up and insulating the exterior of the crawl space, you ensure that the bad stuff stays outside of your building envelope rather than entering your living space.
The recommendation to run a mechanical dehumidifier all the time seems like a good way to add $100/mo to the electric bill, while replacing a $400 appliance every few years (follow up questions: How do you know when it fails? What moisture damage occurs before you figure out it needs replacing?).
If there's any ductwork in the crawlspace, it's common to open some of that into the crawlspace rather than installing a separate dehumidifier. It would be wise to consider the sizing of the HVAC units before doing this however, as you'd be increasing the envelope of the conditioned space.
And really, the crawl space should only be as humid as the interior of your house at that point because it would be fully sealed from the exterior, while also having some amount of air exchange with your living space. If the dehumidifier is running constantly where it's adding $100/mo to your bill, then that indicates a larger issue where the crawl is likely not sealed off properly.
With any of these recommendations, it's far more economical to just pay the extra $100/year in HVAC expenses and leave the crawl space vented/uninsulated.
If you see it purely from a financial perspective, then having it professionally done for thousands of dollars is likely not going to pay off. But DIY-ing the project to bring costs down can make a very large difference in the ROI. Rough cost estimates for a 1300 sqft crawlspace would probably be:
$120-$150 in vapor barrier ($0.10/sqft, but it's typically cheaper with larger rolls)
$50 in tape/supplies
$120-200 in rigid foam panels (27 joist bays per sheet with a bit leftover for smaller areas, plus continuous strips along the rim joists parallel to the floor joists).
Depending on specifics of your design/layout you could probably have your crawl sealed up and insulated for under $400 (below your $480 budget listed in the OP).
And there are non-financial benefits as well (things like more comfortable floors, and inhibiting fungal growth which you indicated was a major motivation for this project anyway).
