You say that the voltage at the + side of the coil was 5-6 below battery voltage. It's supposed to be something like that with the key in the "run" position.
See what the voltage is with the key in the "start" position. It should be at or near battery voltage. If it's not, try hot wiring the coil and see if it'll start. I know someone already suggested this but you haven't said whether or not you tried it. If you did...my goof
You said that the wiring was a mess when you got the car, and it's possible that someone disabled the resistor bypass circuit (which is what you'll be investigating by "hot-wiring")
The ballast resistor is bypassed during start-up simply because the starter is drawing so much that the resistor will drop the coil voltage to a point where starting is difficult.
When you got the car, you had , essentially, two dead cylinders. This would allow the starter to draw less (less cranking effort)- allowing greater voltage to the coil.