SOLVED: (Thanks to this post by krtektm)
Turns out I had to change the port in the config file AND in-game.
Solution: Change port to anything from 49152 to 65535 range in the launcher config file
Then launch BeamMP, go to options > multiplayer, select ‘show advanced options’ and scroll all the way to the bottom. Change the client port to the same port you put in the config file.
Then restart the game.