I'm offering a different perspective.
Once upon a time I owned a 1954 Hetchin's Magnum Opus with "vibrant stays". It rode just fine, and lots of folks thought it was really special, but I seldom rode it. Why? Well, because I felt pretentious and overly self-conscious when I rode it. I decided to find it a new home because the aspects of that bike that caused me to feel that way weren't things that I could address.
This experience makes me empathize with how you seem to feel about the Serotta. What you have going in your favor is that you can change it without ruining the bicycle. If you're self-conscious to the point where it inhibits you riding it, but you also are concerned about preserving "originality" to the point where you can't bear to paint it, then you have a problem that could only be truly resolved by selling it on. Since you seem open to considering to paint it, I'm thinking that this should be the answer.
Pick a scheme that speaks to you and go for it. My preference would be to paint it, but if powder coating works better for you, go with that.
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In search of what to search for.