Do you have the original gray and black ignition coil ?
If you do, I would replace it, it's known as the 'crack-o-matic' coil, for it's tendency to develop cracks in the case .
Usually gives you problems in damp conditions .
Do you have ignition leads with metal caps at the spark plugs ?
If you do, they are original OEM they need to be replaced .
Another problem area, is the starter, at 30 years old, all of the lubricant is either gone, or dried up to where it's not doing any good .
With a 'dry' starter, it takes a lot more power to rotate the starter, at a point, it draws so much power from the battery, there isn't sufficient voltage to operate the ignition system .
My clue was, you can bump start the engine with no problems, but with the starter in use the engine won't start .