the question is, how am I supposed to get it to set the value of stylesheet.cgi's $content to the stylesheet?

I don't understand this question. Context might help. Perhaps you should post some code.

I've tried having stylesheet.cgi print out the stylesheet information at the end, but to no avail.

Well, that's exactly what you should do. You should also print the correct content-type header. Start simple and work your way up. This might get you started:

#!/usr/bin/perl
use warnings;
use strict;

print "Content-type: text/css\n\n";

print <<END_CSS;
body { 
  color: red;
}
END_CSS
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-sauoq
"My two cents aren't worth a dime.";