If you were to put a pfSense Squid Proxy Server with Squid Guardian on a DMZ and then point a cellphone with a 3/4G connection at it for SSL and HTTP with a self-signed CA certificate installed on it; assuming you have control of the phone, would it be possible to point it at the proxy server and keep it there? I realize a transparent proxy is impossible in this case, but assuming you have a static IP or dynamic DNS address it would seem this is possible but I'm not sure.
When you're using a proxy server, it is just that a proxy. Everything will be forced to go through it, whether it is wired, wireless, 2G, 3G, 4G, LTE. The browser is configured to do the following:
phone (browser) --> go to Yahoo.com --> through this proxy (188.8.131.52) proxy --> Internet --> I need this page Yahoo --> Proxy <--> phone
The connection (wireless/wired/mobile) does not make a difference, all your phone would know that in order for it to get to the web, it needs to use this proxy. You will need to ensure the proxy server is always up otherwise no pages would be server.