Plastic Cleaner/Polish....

[lip277]

Hi folks -

I have several illuminated gas station signs that I will be hanging in the shop sometime soon
A couple of them have weathering or abrasions in the surface that shows up fairly noticeably. The lens is colored from the rear - so the weathered surface is just clear - so I think I can just polish the surface to remove the defects... See the two pics below.

Any thoughts on different compounds that might be good to use for this? I figure I'd use a DA/orbital to apply - but don't know what you guys think may be a good choice to start with and what head to use on the machine???
The sign pictured is about 6' square - so it will be a decently sized effort to clean up - once I get to that point.

I have a confession to make... The last time I actually applied one iota of wax or did any serious polishing to a car was probably .... uh.... 1987 or so... LOL
So - I am a bit out of touch that way.
(and yes - that includes the Mustang - I have had that professionally detailed in the past - but my guy moved to Las Vegas - and then had a stroke - so can't give him a call, otherwise I would....)

Any guidance is appreciated.