The tool I use for plastic polishing is my Festool RO 150 FEQ. It is also the tool I use for sanding everything else, including the boat bottom. It does good on polishing plastic, but because of the 5mm stroke it is not the optimal tool for fine plastic finishing.
https://www.festool.com/products/sanding-and-brushing/gear-drive-eccentric-sander-rotex/576017---ro-150-feq-plus
The tool I have also used for fine plastic polishing is the Festool ETS 150/3 EQ. It is superior for fine finishing because of the smaller 3mm stroke.
https://www.festool.com/products/sanding-and-brushing/random-orbital-sander/575023---ets-1503-eq-230v
If the plan becomes retain the existing parts and fix / improve the finish, then it might be required to accept retaining some of the deeper gouges.
If going the repair route my strong suggestion is to retain a flat top surface. It would be very easy to sand away a gouge and have a wavy valley final surface.
A medium or a hard pad will help to retain the existing contours. Do not use a soft pad.
The Festool Granat abrasive sheets are excellent for coarse to fine surface finishing, from 40 to 1500 grit. These have the latest hole pattern for vacuum sanding / polishing, to draw aways debris for extended abrasive life, decreased heat and to avoid clogging.
https://www.festool.com/accessory?mainChapter=26431f61-1243-939b-88f0-06207b4a7b41&chapter=b5431f61-f94c-ee2c-5867-5d7858fb81d0&productChapter=05431f61-2bf2-de59-f694-4668e710fe34&accessoryGroup=c2431f61-21f4-8c6f-ec6f-fcea5fbede74&excludeInactiveProducts=False
The Festool Platin 2 pads are great for polishing, from 400 to 4000 "grit". These are foam pads, but open, permitting the vacuum to draw away debris for extended abrasive life, decreased heat and to avoid clogging.
https://www.festool.com/accessory?mainChapter=26431f61-1243-939b-88f0-06207b4a7b41&chapter=cf431f61-25d6-3267-08c2-699d7209abad&productChapter=12431f61-c5eb-63ae-9cf4-2c40706130fe&accessoryGroup=02431f61-04b2-b1a1-ca1d-3b128a130ae3&excludeInactiveProducts=False
For me, I perform all this work w/ one of their dust extraction tools. IMO bigger is better for more sanding before emptying is required. I use their long life filter bags and dump out the contents to reuse the bag. I get many dump / reuse cycles before the bag finally fails, requiring replacement.
https://www.festool.com/products/dust-extraction
Note that the Festool products are workhorse tools that will outlast the owner. They sell for full list price everywhere, with zero discount from list price available anywhere. IMO they are expensive but worth the cost.
Sorry for the long post...