If you do the first connection with mosh instead of ssh, it will survive vpn/wifi/4g roaming and even system hibernation. Assuming that first hop is a vps in the cloud with a stable connection, you can literally wake your pc from hibernation and once you get any Internet access, mosh will happily restore your "ssh" session for you.

mosh.org: >Mosh will log the user in via SSH, then start a connection on a UDP port between 60000 and 61000.

Needs at least a couple of ports in that range open, because old sessions tend to block ports until they are cleaned.