brycebot Accessing either the full IDE or just interacting with the GUI would work for my situation.
They are both served on port 80 by the on-board http server. This means that as long as you can reach that port on the board you should be fine. Normally, another device on the same wifi network should be able to access it with no problem. If you had a "regular" home ADSL router you could set up port forwarding on the router to access it from a remote place, knowing the IP address of the router on the internet. However I think with 3G routers things are not as easy because I don't think individual devices have a publicly accessible IP address. To circumvent this limitation one could set up some sort of proxy server I imagine, but that is beyond my knowledge. Good thing is that it is a generic application and not Bela-specific. So googling "access server 3g" should be a good starting point.
However you end up doing this, do not forget to add some extra security to your system, as currently anyone who can access any of these boards has complete unrestricted access to your board. One option would be to only allow connections from a specific, safe IP.