Why i'm getting a 404 for PNG in mod_pagespeed
Your RewriteCond:
RewriteCond %{REQUEST_URI} !pagespeedhas two problems with it.
First, QUERY_STRING is a separate variable from REQUEST_URI, and so your REQUEST_URI doesn't in fact contain pagespeed.
Second, it's case sensitive.
So I believe what you meant was
RewriteCond %{QUERY_STRING} PagespeedNote if you're unsure of the case of the string, or if it could be either, you can use the [NC] flag on the end of RewriteCond to indicate that it's case insensitive.