I'm pretty darn sure now that there is a short somewhere in the steering column. It is the only possible thing left. I've checked the starter, battery, non-column wires, alternator, etc. Looks like I get to pull the entire steering column out (for the third time in two years). This couldn't have come at a worse time since the car still needs to get buffed, aligned, decal-ed, have an exhaust fitted, and I just reassembled the entire interior last week. Damn.

So I think I narrowed it down.