Harry ,
I don't know the '64 trim specifically, but I have repaired and polished a fair amount of stainless for my own cars. Probably the most accurate answer is to say that it would certainly be possible to polish the stainless in situ, but it would be a pretty ungainly effort to do so. The compounds used to dress up the stainless would be damaging to either the windshield or any adjacent paint, so you would have to use several layers of protective tape on these surfaces to protect them before taking the polishing wheel to metal. Then you would have to use small buffing wheels to handle them on a drill motor or other such power, rather than the large diameter buffing wheels typically used in a polishing shop.
The small wheels will be much harder to produce a mirror finish with and not show swirls in bright light. And it will take you for absolute ever to get the job done satisfactorily. Further, without taking the stainless off the car, you will not have an opportunity to address all the little dings, scuffs, and deep scratches I guarantee you will find. These need to be worked out from the back side of the trim, and cannot be done with the trim on the car.
Personally, I don't think you are at much risk of harming your windshield at all by cautiously removing the trim around it. That's a commonly done procedure. If you are uncomfortable taking it on, a windshield replacement shop or any good body shop should be able to it in their sleep for you. Might not even cost much if you know good guys in the business. Then the job will be one you're proud of.
Let me know if you need the name of a good repair/polish shop for stainless, and I'll hook you up with someone you can send yours to and count on.
Keith Boonstra
Holland, Michigan
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