When started turning acrylic used this product to polish pen barrels Hut Ultra Gloss Plastic Polish. Think PSI sells a similar product which have not used.
HUT Ultra Gloss Plastic Polish- 8oz-hutproducts.com
People here used to recommend using Brasso on acrylics, have not seen that recommend in years. In my former life used that stuff to shine my uniform & sword brass. Never tried it on a pen barrel!
Due to old eyes, fluorescent shop lights and really needing new reading glasses started taking barrels outside into sunlight before start sanding/polishing with micromesh. Well have new reading glasses and still take them outside!
Have used auto paste & liquid fine compound products if found scratches with varying amount of success when that does not work back to wet sanding!
Sharp tools just partial answer to scratches, lathe speed another consideration. JMHO, higher lathe speed less visible scratches lower lathe speed scratches more visible.