My host (pair Networks) imposes the following limits on CGI resource usage: ...

I'm also at pair.com, and regularly upload files much larger than 35K. In comparing my upload script with yours, the only significant difference I see is that my read loop looks like

  while ( <$fh> ) {
      print OUTPUT $_;
  }
[download]

instead of

  while ( read( $fh, $buffer, BUFFER_SIZE ) ) {
      print OUTPUT $buffer;
  }
[download]

Should that make a difference? At first glance, I don't see why it should. I might be on a box that's configured differently than the one you're one, or the box might be more lightly loaded.