Using mosh with Back to my Mac
I got it working.

It requires a bit of messing with mosh, so try it first with the current version before hacking with your installation of mosh. Leave a new answer or a comment if this starts working with the latest versions of mosh please.

First, on both the client and the server, install the latest version of mosh: brew install --HEAD mosh. 

Then edit the mosh file ($EDITOR 'which mosh' (use backticks instead of single ticks)) as specified here: https://github.com/keithw/mosh/issues/81#issuecomment-57074800 
I made the change on both the client and the server.

Then execute mosh -6 your_server if you followed Rnhmjoj's suggestion, or mosh -6 your_server.you_magic_number.members.btmm.icloud.com