Turning key to "run" causes all power loss.

Before going too far, track down the initial probem.

I've not seen an AGM with a built in breaker. I can say from experience that they do not like high charging rates. They get hot and stay hot (because the liquid is captive in the matting) when charged at 20 amps or so for 15 minutes. Bottom line with a severely discharged battery use a battery charger not the alternator if possible especially when dealing with an AGM.

20 amps for 15 minutes is a bit much for 16 gage wire at the crimp. Even the heavier terminals and wires may get hot.

Side note: '67 FSM says a voltage drop of .3 V is max allowed between the alt and the battery for a 10 amp current. My point is that even the factory knew there was resistance in the circuit with the distance in the engine bay, all of the junctions and the fusible link. I suspect it is why the alternator feeds directly to a welded splice with the only connectors being the ring terminal at the alternator and the push-ons (Packard 56/58) at the firewall. (In 1975 they split the feed through the firewall to reduce the maximum load on the connector. Heavy duty alternator optioned cars also split the load)

Short to ground. The only protection on a '74 was the 16 ga fusible link.

With the '74 seat belt interlock there are a bunch of wires going to the control unit including a start wire from the key switch. I haven't studied the details but its possible the loose connector and cable could be grounding out when the key is in start.

IIRC '74 also has an 'engine connector' to ease factory engine installation. R6 may even go through it (and if so that would make my statement in the side note innaccurate for '74). These are often a problem location as can be the steering column connectors.
The battery was failing to turn the engine over Saturday morning after several attempts to start, so I put it on my Schumacher smart charger (AGM mode) on Sunday and it was reading 100% charge by Monday evening. It was likely ready long before then but I didn’t check it since I knew that I didn’t have the new wiring stuff yet.

I agree with the AGM and breaker. I only mentioned that because when my household GFCIs trip, the voltage at the outlet is in the low single-digit or double-digit range rather than at zero or at full 115-120V. It was odd that I could measure 0.3-0.6V at the ignition switch, hence my thought that a similar safety switch had kicked in.