I have a question for you sir. IF BiaB used 6/8 time as the other software companies and not 4/4 time would the tempo have stayed identical?
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?
Somehow Band-in-a-Box is interpreting the time signature correctly when the MIDI file is imported. We could take a look at the data in the MIDI file if we had it. There are some meta events that may or may not be present.