Overcharging
This car has been botched a lot, I think the problem of the voltage drop is from the ignition switch. I am going to get a new one and try this one first. I have been thinking about running a separate wire.
Why not measure where the drop is rather guess?
With the engine running, battery fully recharged, measure the drops at different access points (backsides of connectors). Then do the same with turn on some additional loads (like fan, lights).
Do the same with key on, or lights and engine off if you think there is resistance in the line from the battery to the main splice.
The downside of installing a relay for the run circuit is that the rest of the circuits may continue to see the voltage drop in their supply.
Lets say there is a 1/4 ohm resistance in the alternator output's bulkhead connection, .1 ohm in the battery feed's bulkhead connector, another .1 ohm in the column connector, and .05 in the ignition circuit's bulkhead connector.
Installing a relay for the ignition will get the alternator to produce at the correct voltage and remove 3-5 amps load. But current for everything else will still be going through some of those high resistance connections. Stuff like the brake light, headlights, dome light, heater fan, batttery when it needs charging, etc. So that stuff will still see voltage drop whenever they are turned on.
Since your car's wiring has been modified, sketch out what you have. Feel free to borrow any of the diagrams I've posted and modify them if. Best if you refer to the FSM for your year/model/options. That way you'll have the correct colors, connections, etc. If you like doing some of the drawing on the computer, MS Paint is all that's needed and save as a PNG file.