Good tip, Clay!

My friend Clay suggested that I confirm that the vacuum and mechanical advance functions were working on the distributor.  Turned out to be a good tip.  Here's a section of the vacuum line that had fallen behind the motor and gotten burned up:

It was sealed, so at least it was not a vacuum leak.  But the distributor was definitely not advancing it's timing with vacuum increases!  Guess there's a reason the factory made these lines out of metal.

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I patched it back together and checked it's operation with a vacuum pump and found that it still did not work because the small spring that connects the vacuum diaphragm to the distributor plate inside the distributor was disconnected.  Got that repaired, went out and drove car, and it's much better.  Still want to confirm dwell and timing adjustments and then fine tune the carb settings, but we're getting much closer now.