The first time you set this up would be time consuming.
But if you really need to stay in Biab:

On each BB track in the VST window Save each track FX with Save Group.
In REAPER just save it as a default BB FX project.
You can setup
Track 1 ReaStream 1 with a different set of FX
Track 2 ReaStream 1 with a different set of FX
Track 3 ReaStream 1 with a different set of FX

Track 4 ReaStream 2 with a different set of FX
Track 5 ReaStream 2 with a different set of FX
Track 6 ReaStream 2 with a different set of FX
....
....
and the same for the other Reastreams
then you just solo the track that you want to use for each track send from Biab.

So you have REAPER running each time you start Biab,
after you have the Biab song generated open the VST window
and Load Group for each track:
Track 1 Reastrem 1.tgs
Track 2 Reastrem 2.tgs
Track 3 Reastrem 3.tgs
Track 4 Reastrem 4.tgs
Track 5 Reastrem 5.tgs