Band-in-a-Box does support 6/8. From the OP's screenshot, I can see that it says, in Guitar Pro, "quarter note = 204". This is what I'm going on. It should really be "dotted quarter note = 136". Are we in agreement?
Hmm, this probably highlights the problem.
Unless I'm mistaken,
the MIDI specification defines set-tempo as microseconds per quarter-note, so I think it does not have offer the dotted-quarter-note option. Do please correct me if I'm wrong.
I think it gets more complicated still in XML, where tempo for the sound element is specified in
"quater notes per minute", but there is a separate
"tempo type" for the performer. That may be where the dotted-quarter is handled, but I don't actually know and I couldn't quickly find a clear explanation.
There's also another issue. Dotted quarter note implies the rhythm has downbeats on the 1 and 4 of the six, which is pretty usual, but not always true. It can certainly vary with some other time signatures.