This ought to “just work”. The list of tunings should include custom (user-defined) tunings as well as the built-in ones. For example, I followed your steps and modified the 5-string bass guitar and then I got this:
Note the “5 Strings: B2, D3, G3, B3, E4” tuning in the list. The only slight oddity here is that you will need to save, close and reopen the project in between changing the tuning for the instrument and trying to set the chord diagram tuning. This is an awkwardness with how the menus are built up.