What are the considerations for crawlspace encapsulation barriers / humidity control?
I use a standalone humidity reducer in the wettest room of my house. I've used one in a finished basement too, when it got too damp down there we ran it. For about $100 USD you can get a decent dehumidifier that plugs into a regular wall socket. It works by pulling water from the air. They also produce heat, which will raise the room temperature a little when it's running, helping the drying process. Most of them have a way to attach a hose and run the water directly to a drain if you don't want to manually empty the bucket. Otherwise you'll have to empty the basin a couple times a day when the room is very wet. I opted to buy a larger machine with a bigger collection basin so I don't have to empty it as often.

$5000 to throw heavy plastic over the crawlspace floor sounds ridiculous. We had our whole basement cleaned, insulated, and sheeted over dirt floors for less than half that cost. You might want to get a few more bids or consider a DIY.