Do you have termite contract on your home. If so, that company can do it. Call Neuse Termite Or Wood Termite if you do not already have a company
I've seen these guys do some amazing work - http://www.crawlspacedoctor.com/ Unfortunately they are probably more than $3750. That's pretty cheap.
$3750 for a vapor barrier? I hope you meant $375, which is what Neuse Termite charged me last September for a vapor barrier installed. I would have done it myself, as it is not that hard or labor intensive, but it was for the closing on the house, so I let them do it "professionally" to satisfy the buyer. How big is the footprint of your house??? Are you sure you didn't get quoted for sealing the crawlspace?
If you only want to put down a piece of plastic, it should only cost you like $50 from Lowes. If you want to seal your crawlspace like this, it is usually between $2,000 and 5,000 depending on the size and complexity.
That's an impressive crawl space. I always wondered if you seal the crawl space then do spray foam insulation, how does the house "breath"? I would think without a certain amount of air moving you will trap moisture and have mold.
Tatum insulation does crawl spaces, both for sealed and traditional style crawls. Cost is going to be more than 50 as we use a 6 mil or 10 mil poly. If you give me the square ft estimate, I can get a quote. It would help to have a picture of the height of your crawl. A small, low crawl would cost more for the tight working conditions, but a average to tall crawl would be cheaper. (Because of hourly wage) Pm me for my number to text picture
Depending on the size of your crawlspace it should only be a few hundred dollars, sealed crawlspaces are much more expensive.