Tor services do not require port forwarding. So, maybe...
Run Tor service on Raspberry Pi at home, that is basically just a proxy. Connect to that service from phone via Orbot.
Comms between phone & proxy are anonymous (over Tor).
Comms between proxy & shared router & internet are same as if you were on your home computer (assuming just a simple proxy).
Not sure if that would meet your needs. Also not sure how to setup that Tor service, but seems possible in theory.