I don't know if this assists Lloyd, and it seems you have probably tried it, but if you can hear BiaB through the system's speakers, then you should just need to experiment with Audacity Recording Device settings to record the system's speakers:

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BIAB & RB2026 Win.(Audiophile), Windows 10 Pro & Windows 11, Cakewalk Bandlab, Izotope Prod.Bundle, Roland RD-1000, Synthogy Ivory, Session Keys Grand S & Electric R, Kontakt, Focusrite 18i20, KetronSD2, NS40M, Pioneer Active Monitors.