I have to agree with TheCrownedPrince about the Lustre King. Unless the owner of the center guarantees that it has polish and not wax, I would never use one.
With that polsihed pearl "fusion" I would not stick it in any polish machine unless the cover started to get dull.
And even Clean and Dull won't restore a wax clogged ball IF that is, indeed, the problem.
I'd have it re-surfaced to try to clean out the top layer of resin, have it baked in a Rejuvenator, then have the surface restored to its original Lane#1 specs.
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"None are so blind as those who will not see."