First, thanks for all the suggestions.

I have an idea, but I don't know if it'd work. I may have access to NuBus connectors at my local surplus store (I'm going to go check today.) What about soldering a molex connector directly to the voltage pins on the card, disabling the pins underneath so they don't connect to the motherboard, then just plug it directly into the LC power supply? Give it its own dedicated power supply. Avoid modifying the motherboard or splicing the power supply all together, and make the modifications to the card itself.