Hi scale,
This is why one leaves BBs well enough alone if he/she can get away with it.
It's interesting that the spots of resistance and looseness aren't the same with each revolution. Did you put in more balls or balls of a slightly different diameter than the stock configuration?
If the looseness/tightness are minor, you might be fine just riding the thing. The situation will improve as the parts break each other in. But you'd do well to service the BB sooner the first time to get out the worn metal.
If the cups and/or the shell aren't well, your choices are few and mostly expensive. If it's the cups, you might be able to score some better ones off of a dead parts bike. If it's the shell, you're likely looking at re-tapping the shell to a modern threading and putting in a modern crankset. The latter will total the bike by far, but if it has sentimental value, it wouldn't be entirely unreasonable.
(I'm running a Phil Wood BB and Sugino crankset in my '74 Raliegh.

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