In Chicago the subsoil temperatures are well below the average dewpoint of the outdoor air, so when that air enters the much cooler crawlspace it's relative humidity climbs through the roof.
The primary source of the humidity is not a mystery- it's the outdoor air coming in the vents! The average outdoor dew point in Chicago is in the mid-60sF, and the deep subsoil temp is around 50F, so in the summer the crawlspace will run much cooler than the outdoor air, with heat being pulled into the soil. The air temp in the partially-vented crawl space may run 68-70F even when the outdoor air is in the 80s unless the ventilation rate is extremely high (not likely, with passive vents). With an outdoor dew-point of 65F, cooling the air to 70F yields a relative humidity of ~81%. When the outdoor dew points hit the 70s (which does happen in Chicago), the relative humidity is higher still.
If it doesn't stink like sewage down there, only moldy/musty, it's highly unlikely that you have a contribution from your house drains, and the $199 inspection is a waste of money.
If you're running a dehumidifier in there with the vents open you're using 3-10x as much power as you would if you seal up the vents, since with the vents open you're trying to dehumidify the whole great-outdoors. If you seal the vents (highly recommended in your climate, even if code requires that you make them operable to vent after a flood) it's also important to put down a ground vapor barrier sealed to the foundation walls to control both ground moisture & other soil gases.
You can use 6-mil poly (10 mil is better), as a vapor barrier, lapping the seams between sheets by about a foot, and sealing the seams with duct-mastic (normally used for sealing heating/cooling ducts, available at box-stores). At the foundation walls run it up the wall by about a foot and hold it in place with furring through screwed to the foundation with Tapcons every few feet, sealing the edge with duct mastic. In most Chicagoland homes it would also be cost-effect from a heating & cooling cost point of view to insulate & seal over the foundation wall right up & over the foundation sill & band-joist with 2" of closed cell spray polyurethane (spraying over the vapor-retarder furring is OK), but that can be treated as a separate project. Even with the vents closed up, the air leakage into the crawl at the foundation sill & band joist is significant, and insulating over them with ccSPF makes it pretty air-tight.
In general vented crawlspaces ADD more humidity than they remove in most US climates east of the high-plains east of the Rockies. Though it was required by code for decades, there is little science behind it, and it's inappropriate for climates with summertime humidity as high as Chicago.
Pouring concrete in the crawl (even a non-structural 1-2" rat-slab) is a good idea. But down 3" of 1/2" screenings/pea-gravel, then a 10-mil vapor barrier, with the concrete on top of that. The gravel is a capillary break & drain, mitigating liquid water from ever coming up through the seams in the vapor barrier, and the concrete protects the vapor barrier. If you're planning to insulate the foundation walls, adding 1-2" of rigid EPS insulation under the slab between the gravel and vapor barrier is cost-effective in the long-term.