Using the VST with Reaper, I made the Band-in-a-Box track a parent to the tracks containing the MIDI it generated. Once I had assigned instruments to those tracks, I noticed that the output level from the parent was much louder than the level being passed into it. Soloing instruments showed me that Band-in-a-Box was adding 6db just by being present.

The obvious fix is to remove the parent/child relationship (or to disable the Band-in-a-Box plugin after generation). However, I'm curious about why the gain increase happens. I don't see anything in the VST that looks like a control for it.