Eureka! I was able to unbury a deleted reddit comment about a similar issue, which instantly solved my issue. Specifically had to change the Initial Display Output in BIOS from PCIe 1 Slot, to IGFX (and plugging the display cable back into the motherboard output).
Not motivated enough to re-try this fix with the old motherboard/cpu in to confirm this would solve the issue for that hardware as well, but I think it’s safe to assume.