You have a good amount of vents. Nothing is blocking the vents (which are about 9" x 12"). The crawl is a full crawl. Each room above the crawl can control its own heat. THEN YOU MENTION: When the house is shut up in winter time, the one room has a musty smell, and the carpet feels damp.
You didn't mention that before. It makes a HUGE difference. Heat will raise the level of humidity. (Warm air holds more moisture than cool air.) And if the house is shut up, where's the humidity to go? Baths and showers, boiling tea water, running a clothes dryer, burning a heating stove, and the like, will all warm the house and generate moisture. If the moisture happens to 'gravitate' to one particular room (you say 'one room'), then when that one room cools (as it would in Winter), all your moisture will settle out in that room ESPECIALLy if the floor is cold.
I'd bet that the room you're referring to is a corner room on the South side of the house that has little 'traffic' in it. If the house is as tight as you imply, your solution is to run the dehumidifier whenever the house is in use. Leave the doors to all rooms open (most of the time) when the house is occupied. Insulate the floor as I mentioned. There's no need to go nailing up any plastic or anything.
It just sounds like the house is real tight and you're generating a lot of excess moisture that isn't getting removed (via the methods I've given.) I don't know where you live. In some parts of the country, it's recommended to close the vents off in Winter. Check around and see what you can learn.