"I could just type in my chords, set the style and let the program go, but then I don't get to hear the solo against my backing track."

You could make a copy of the original .mp3 and rename it to the same as your song in BIAB (if it is different) and have BIAB play the .mp3 as an audio file. Then if you have typed in the chords in BIAB for the song correctly - and since you have the book with them it should be correct - you can generate the solo(s) in BIAB and mute all of the other instruments so only your soloist and the .mp3 play. That might work.
Good luck.