"1964 Impala with the stock 283 and only 39,000 original miles"

A 1964 with only that few miles,,are you sure of the mileage??
The heavy oil build up would suggest higher mileage,,but could be from being driven real slowly all it's life and getting realy hot.
If that is the case,,then i'd suspect the engine of having major carbon buildup in the intake and the rest of the block oil gallerys may be realy plugged.
I would take the oil pan off,,and the valve covers, along with the intake manifold, and get a good look at the motor.
And also a compression check as previously suggested.