Good post. Well written with lots of good trouble shooting already done.
The ballast resistor will drop the current flow in half. The street fire coil most likely will have about half the primary resistance as an old round coil, which will double the current flow.
So your current flow is about 4 times the stock IGN system DS2 module was meant to handle. Thus a HOT DS2 module.
The only ideas I have on getting the 4 pin module to work is be sure and add an extra ground on the mounting screw the has the metal inside it. It is on the left in your photo.
Also try swapping the to stator wires on the 4 pin module to see if it helps.
To get the DS2 module back on line you will ballast resistor to lower current flow to the DS2 module. An old round coil would also help as it has a higher primary resistance, 1.2 ohm,
The ballast resistor should be close to equal the coil primary resistance, to divide the supply voltage equally, 6v and 6 volt.
A 1.2 ohm ballast with a .6 ohm coil PRI will only leave 1/3 of the supply voltage to the coil positive. Say 8 Volts and 4 volts split. It might not run with 4 volts supplying the coil.
Jim