I don't have a good direct solution to offer up, but think a manufacturing change in springs might be giving you problems.
The outside end of the spring configuration changed slightly around 1978 when the starter spring retainer was introduced -- likely incidental. I'm guessing the two springs are sold as interchangeable.
However, the fit may turn out to be a problem in some cases -- maybe yours. In that sort of sappy video, the outside end of the spring is apparently bent to better hook onto the cup. I can't tell exactly from the video what spring it is. The older style had sort of a flattened hook that presumably fit up to catch the cup edge. The newer style probably had to be pulled out from the cup a bit to make sure it stayed in place. (I think there's a pic on LeRoy's Ramblings somewhere that shows a spring end extended out about 3/4" or so outside of the cup -- might be a new styled spring used in an older cup, but guessing at that. I don't think it was engineered to hook around the cup edge.)
Depending on what's happening with yours, it might also be possible that the washers on the top and at the bottom are not in place -- that there is too much vertical play in the fit of the spring, allowing the outside end to slip out of position.
