Problem solved!
After consulting with another LX owner on an LX570 Facebook group, he figured it out. We both had exact same troubleshooting steps: checking all the fuses, under-seat connectors, switching out ECU and the only thing that was missing was a plug that was located behind the seat-back area. See pics below:
This is what it looks like after you remove the back cover of the seat. It's a relatively straight forward process. Loosen two bungee straps on the bottom, remove two screws in the mid-section, then pull the backing downward to remove.
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After taking off the back cover, there's one white plug that's right next to the vent. Upon a closer look, the wires attached to the bottom portion of that plug had somehow broken clean off.
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To fix this issue, I had to break off the last hanging wire, re-pin the entire plug with new wiring and then solder the new wires onto the existing wiring harness.
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To remember which colored cable goes where, I marked the original locations with G (grey), Gr (green), B (blue), and R (red).
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I added some solder to the pins to ensure the connections are secure.
Now solder them to the existing wiring harness.
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Once that was done, I plugged it back in, and Voilà! The heat/vent both work now. I hope this helps those who are still struggling with their broken seat climate issues.