How about keeping connection open from the webcam server or any host on the same LAN with a ssh reverse tunnel to a cheap cloud server?
For example when the webcam server is reachable on LAN at 192.168.1.2:1337 you can do
$ ssh -N -T -R 1338:192.168.1.2:1337 user@cloudserver.com
on a raspberry pi on the same LAN or locally in the webcam server and then you can access the webcam server from anywhere using cloudserver.com:1338