What you are saying makes no sense at all. A 12V battery that ever showed as low as 6V would never crank the starter in the first place. I think either you've got a flaky meter, or didn't get it well connected. If not that, I don't know. This is not rocket science. There ARE coils made to run without resistors, you need to go to the source (store?) where you got this coil and find out. Virtually all 12V CARS and LIGHT TRUCKS from the first 12V to present run either a ballast resistor or "resistor wire" in the harness. This means that they are not truely "12V coils" they are "12V with the proper resistor" There are OTHER "general purpose" (industrial and tractor) coils sold that are designed to run directly off 12V.
Can you post a diagram? If nothing else, draw it out, take a photo, and use "tinypic" http://tinypic.com/
to post the diagram.
Ammeter, doesn't the tractor have one? Basically, ONLY the battery connects to one side, everything else, gen/ alternator and all loads, come off the other side
Alternator? single wire (I hate those things) Three wire? How is it wired.
Wrong ground polarity? Take a **** of a good look at the battery and cables. There's only ONE right way to run a 12V system, and that's negative ground. Was the battery every COMPLETELY dead? It IS possible, if someone is a complete "tool" to discharge a battery and then charge it back up the wrong polarity.
Find another meter. Find a friend. Take some more readings, and make SURE This is not rocket science. It's tractor science. I could do this when I was 13 years old. And I did.