Gee, with all the successes just applying polish on top of the stock 4000 grit Abralon surface, I hate to say what I was thinking ... but what the heck.
With balls already at a very fine 4000 grit Abralon, if you're thinking of adding polish, I usually suggest taking the surface down a bit, to at least 1500 or 2000 grit Abralon (sometimes even lower) and then applying a light coat of non-abrasive polish.
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"None are so blind as those who will not see."