In case you use ever changing outbound public IP connection like in Microsoft Azure, then you can try create machine with public IP and passing your local traffic to remote site via simplaproxy. L switch is for local and R is for remote.

simpleproxy -L x.x.x.x:YYYY -R someremotedomain.remote:ZZZZ -v

To make it durable you can try creating systemd service or keep it open on screen session.