How to properly configure the PageSpeed ​​cache for linking with the CDN?

Question

htaccess

Friends, help me, I'm completely confused.
So there is site.com, site.net, site.org, and they are all different sites. For them, a CDN is raised through MaxCDN, the static.site.info domain is made. All this physically on one server. All work only through HTTPS.
Static files are launched via rewrite:

RewriteEngine On

RewriteCond %{HTTP_HOST} ^site\.com$ [NC]
RewriteCond %{REQUEST_URI} \.(jpe?g|png|gif|svg|css|js|eot|ttf|woff2|webp?)$ [NC]
RewriteRule ^ http://static.site.info/cache/com%{REQUEST_URI} [R=301,L]

All statics are physically copied to the right place (so as not to holivar - sites have files with the same name, but with different content).
Mod_pagespeed is running on the server, CDN has been added to the config:

ModPagespeedEnableFilters rewrite_domains
ModPagespeedMapRewriteDomain static.site.info/cache/com site.com

How do I get everything mod_pagespeed glues and generates to go to the CDN?