You don't need to make the HTTP port accessible from the Internet at all for remoterig to function. Once set up, you don't need access to the HTTP port from the Internet; only the UDP ports are required.
Also, I wonder how the remote is accessing the network. If you're using some kind of access point, perhaps as wifi client (which is not unlikely given the unavailability of the wifi module these days), you might want to ponder using said access point to create a VPN tunnel and only make your remoterig accessible via the tunnel. I would do some experiments with OpenWRT for this.
Alternatively, if the control station is at a fixed location (hence has a predictable IP address), you can limit access from the internet to only accept these predictable IP addresses. That is trivial (at least on OpenWRT).
If you DO need HTTP access, another possibility would be to make an SSH connection to a raspberry pi, enable SOCS on the SSH connection ("ssh -D 1080 ....") and then temporary enable SOCS on your firefox browser and use that to access the HTTP port. Note that you can't use SOCKS to tunnel the UDP connections but HTTP should work.
