rewire the alternator

Either doing this the "mad" way or jumpering right to the starter relay, YOU STILL must have a clean path of "so much" power inside the car. That is where heater, lights, "everything" comes from. So if you simply jumper the alternator to the starter relay, you have not fixed the bulkhead connector problem

Also "in this mix" and NOT fixed by either method is voltage drop in the ignition switch connector or switch itself, and of course the ignition voltage must go "out" through the bulkhead connector and THAT is another potential drop

"One way" to fix / work around that is to use the "run" wire to trigger a relay, and feed all loads off the relay