Okay, I’ve got a partial solution. (Meaning this is probably not what you’ll want to use, but here goes…)
In Setup Mode navigate to Edit Instrument Definition. Then set the instruments’ transpositions from Bb to A#. The good news: it gets you key sigs for Eb minor. The bad: you now have "Trumpet in A#.
(I did this for Tenor 1 and Trumpet 1 in a blank big-band template chart, and as you can (partially) see, it changed both instances of the tenors and all four of the trumpets:
(I’m really hoping that someone who knows better how to achieve this in the “boundary case” of 6bs/6#s will jump in and share the solution.)
ADDENDUM: Towards a solution…
Now Rename Player…, which will let you show " "Trumpet in Bb in the parts layouts:
Then Edit Names… to set the Show transposition to never.
This will hide the "Trumpet in A# in the score layout (which I cannot figure out how to change — is there a way?), which I would be okay with doing in a jazz big band score, where it’s assumed, but I’d not be comfortable doing in an orchestral score.