The Axolotl key management algorithm was jointly developed by Moxie and Trevor Perrin. Both of them are widely respected in cryptography, and the protocol has undergone formal cryptanalysis.
A novel crypto algorithm someone puts up on GitHub is "home-brewed." The Axolotl algorithm can no longer fairly be described as "home-brewed."
Just use XMPP.
(^) Granted, moxie can be considered a crypto expert, and the design got some public auditing.