I used a sanding block and my cheap car orbital buffer. I had forgotten I had one
Worked great to buff out the plastic.
Just some thoughts on all this:
I have had some success repairing hazed cloudy & scratched TT dust covers, my approach is to precede the task with an initial careful assessment so as to develop a simple workable plan based upon the many variables.
The idea here is to avoid going in like a bull in a China shop and recklessly making your cover worse and then regretting destroying what was initially a reparable (hopefully not irreplaceable) item.
There are widely different types of clear cover materials (polymer resin chemistry) depending on the makers' design parameters, construction methods and cost constraints.
Blow molding, vacuum forming with heat, injection molding, fabricated with glued edges, etc., and then there is material selection:
Acrylic based
Styrene based
Polycarbonate
Polyolefin family:
(LDPE) low density polyethylene
(LLDPE) linear low
(MDPE) medium
(HDPE) high
(EVA) ethylene vinyl acetate
(PP) polypropylene/ propylene copolymers
Each material has specific engineering properties and surface characteristics.
Some develop top layer surface barrier-like films in their manufacturing or within the mold cavity, which when cut though in polishing can reveal optical boundary separation artifacts.
One should assess how deep the resurfacing needs to go.
No need to polish far below the damage depth range.
Polish/rub too aggressively, and the heat generated can cause deep irreparable hazing/fogging/stress marks/crazing etc.
Many/most (non-glass) auto headlight lenses are Polycarbonate based for resistance to stone impact fracture, as per DOT, and due to the anticipated exposure to high heat, extreme UV radiation, pollution, and harsh chemical contact including exhaust gasses, brake dust and car wash detergents, these covers are factory sprayed with a VERY HARD clear 'paint' and baked for curing. I found this out the hard way polishing the plastic headlights on my 96 Impala SS. This coating was extremely hard and difficult to sand through, and once I penetrated a small spot, the entire surface needed to be done to eliminate the huge edge effect (at the coating line) that was visually unavoidable.
Polishes contain carefully controled sizing of tiny hard abrasive particles that physically remove material producing a newly lowered and optically flatter top surface in order to eliminate previously observable irregularities and imperfections.
Obviously it is critical to diligently rinse ALL coarser abrasives away before moving on and cross-contaminating the next step using a finer grade compound.
It is also foolish to use too coarse a grade initially (like 220) just to remove very light surface dust marks and swirls. With a lot of labor, it can get you a good result, but unnecessary material removal (and hard work) can and should be avoided.
I usually start out 'in reverse' with a quick test, by hand rubbing some compound on the worst area using 3M Finesse-It II #05928 just to see what it does NOT remove, and if that test is not completely effective, I then move on to 3M Perfect-It EX #36060 to see if that will cut deep enough, this test can help me see if I can skip the need for sanding.
Wax applications serve to 'fill-in' scratch damage with optically transparent material to restore the original surfaces' optical performance.
Like wax, windshield repair liquid resin repairs fall into a similar 'filling-in' category, only doing that job much more permanently.
Block sanding, working progressively finer toward eventual optical clarity can produce a surface even more flat than original, but if the inside surface is not also perfectly flat, such that the inner and outer surfaces are dead parallel, then the result can be optical anomalies.
Finally, A HUGE obstacle is having to work around those permanently molded-in logo plates usually found in the middle of the top panel!
.... Man, that issue is always so frustratingly hard to overcome, because in the end we obviously want the new perfectly clear surface to mate up perfectly to the pre-existing edge of the (hopefully) untouched logo plate!!!
That's why I love a TT cover that has no logo plate on it.
I hope a few of these thoughts are of use to someone here.