Turning key to "run" causes all power loss.

My 74 Valiant had a faulty ignition switch (it wouldn't send 12V to the starter relay), so we replaced it with a new unit. That one was faulty from the start (you had to hold the key juuuuust right to get the starter to turn on), so we made arrangements for a replacement. I hooked up one of those handheld switches to the relay so that we could use the car. In the meantime, the new faulty switch began to cause other issues. The ammeter stopped working (it always reads 0A). But the car still ran. Then it didn't. The button would still turn on the starter, but the engine would never catch. I found that I had no spark. And only 0.3V to the positive side of the coil while the key was in "run". And then I found that none of the electrical items were working: blower, headlights, etc. I checked 12V at the battery, but only 0.3V on the wire going to the ignition switch. I disconnected the battery and suddenly I had 12V at the ignition switch again. But when I turned the key to "run" all voltage drops to 0.3V. I finally got the new switch and installed it today, assuming it would fix the issue, but it did not. I can let the battery sit for a few minutes, then disconnect it and reconnect it, and I will have 12V everyone again. But as soon as I turn the key to "run", I get nada.

I've tried:
1. Disconnecting all engine-side wiring that comes from the ignition "run" position: voltage regulator, alternator field connections, ballast resistor (both resistors), and ignition control module. This still gives the same voltage drop.
2. Probing the switch wires. I checked the switch operation. 12V source (red) to yellow and brown on "start". 12V source to black and blue on "run". 2 small red wires run to the key-in-ignition switch and are good. 1 orange wire provides illumination voltage to the lamp on the gear indicator. The new switches came with a small black wire that was not active on any positions. Not sure what this one is for. I taped it off.
3. Disconnected fuses. I disconnected 4 of the 7 fuses in the driver's side fuse box. Each fuse passed a continuity check. This still cause a voltage drop. I reinstalled those 4 fuses and removed the other 3 fuses. They likewise passed continuity and I still have the voltage drop issue.

Ideas for next steps?

I have the FSM for the 72 and 73 Dodge and Plymouth stuff, so I'll likely continue to use that schematic to move down the line. I assume that I have some sort of massive short and the battery (AGM) has some sort of fail-safe circuit breaker built in.