Using ReaStream https://www.reaper.fm/reaplugs/
Load Reastream vst into Biab on the first track set the identifier 1 (each track different 1,2,3,4 etc..) and set it to Send > *local broadcast
set the identifier the same for the corresponding REAPER track and set it to Receive, put a gain control or 2 after the ReaStream vst in BB so BB makes no sound only REAPER https://www.bluecataudio.com/Products/Product_GainSuite/
it's lighter than Bluecat but you may need 2 to cut the volume off, then chain up the FX in REAPER.
Turn any reverb or tone in the BB mixer off.
You can set REAPER to loop play if you have no sound.
If you need to run multiple ASIO https://www.vb-audio.com/Voicemeeter/banana.htm
EDIT: In Reaper Preference > Audio you can set it Always On by unchecking, see pic below.
Check the video out:
I haven't worked out midi with ReaStream I think that is just Biab doesn't have midi plugin chain, so to send midi for Mac you can use midiOut.dll
Click the Softpedia Secure Download (US) link not the external, for Win https://www.dropbox.com/s/ifc0waq0qdusb3z/midiOut.zip?dl=1
and use LoopMidi
and set it to LoopMidi Out then set Reaper track to LoopMidi In, for Mac just create a virtual midi cable.
The first time you set this up would be time consuming.
But once you save it all next time will be quick.
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
Once it's all sounding good and you have the tracks how you want them just drag export each track into the corresponding REAPER track and Render.