<<< Is there a universal simple setting that would separate two things (BIAB mixer / Halion mixer) into independent sources for future songs? >>>
Not setting but setup, yes. Use the BIAB VST/Halion VST into a DAW and port each track from each VST individually to a track and output to your interface. You could also accomplish the same with a digital mixer with a multitrack interface. The Behringer XR18 would give you 18/18 in/outs for $500. Each track would be independently controlled by its software and you'd control the outputs, Fx's, levels, panning, mixing and routing with the mixer. Similar results can be obtained from a Control Surface such as the Behringer XTouch but you'd still need a separate audio interface to control everything.