Try the rubbing compound, but after try some toothpaste. It will be finer and give a better polish.
Years ago I had a Seiko automatic watch. When the crystal (acrylic) got scuffed I would use toothpaste and it would look like new again.
If the plastic has yellowed, it is likely styrene, not acrylic.
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1971 Paramount P-13 Chrome
1973 Paramount P-15 Opaque Blue
1974 Raleigh Professional Blue Mink
1991 Waterford Paramount
Holland Titanium Dura Ace Group
Holland Titanium Ultegra Triple Group