Reducing the thickness by squishing it to fit would reduce the R-value, in which case, you might as well buy insulation with a lower R-value that will fit into the joist space. In our area (Central Texas,) R-19 is recommended for crawl space.
Other than finding some way to rig your floor framing to fit the insulation such as replacing the joists with thicker ones or adding on to the existing joists or loosely draping nylon mesh under the R-20 insulation so that it doesn't compact the insulation, my husband thinks you're better off using a lower R-value. Most heat loss is through the attic. The greatest benefit from crawlspace insulation is air infiltration control as opposed to heat loss control.
In answer to your question about putting down plastic, my husband says, yes, but even more important is adequate ventilation through the underpinnings. A lot of this depends on where you live.
That said, he remembered an article in the August 2004 edition of
The Journal of Light Construction about how to control moisture in the crawlspace by sealing it. This method also eliminates the need for insulating the floor because you seal the ground and insulate the crawlspace walls instead. Here's a link to the article:
http://www.jlconline.com/cgi-bin/jlconline.storefront/4217601f000e845a27187f0000010535/Product/View/0408fixi You have to pay $2.95 to read the whole thing if you're not a member but I have the article here if you'd like me to copy it and fax or mail it to you.
I hope this helps! :hi: