DannL- Consider yourself fortunate that something much worse didn't happen to you or the car.
I had the exact same problem with my 1929 Hudson. The new cutout points were just as bad.
With the engine off and the points stuck closed, the battery directly shorted right though the generator. A fire ensued in the generator, which is located directly below the updraft carburetor.
I stopped the direct short by pulling the 14 gauge wire from the cutout with my bare hand, in the flames. I then beat the flames down with my jacket and bare hands. My adrenaline was pumped so high that it took more than an hour for me to feel the pain caused by the wire cutting into my hand, and some burned off skin.
I fixed the cutout by replacing the mechanical points with a diode. This event happened more than 20 years ago, and I've never used mechanical points on a generator cutout since that event.
The failure more of a burned out diode is your generator will stop charging the battery.
The failure more of mechanical points stuck closed can be catastrophic.
I hope that other folks will learn from this experience, and replace the mechanical points on their Model A generator cutout.
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