Melt it.
Really! [ But, remove ALL chemicals, waxes, Polymers, etc. from the surface of the cladding before trying this. ]
If it really is plastic it was heat that put that shine on there, in the first place.
Do NOT use a torch, of any kind. Just hot air will do the trick.
I would try the wife's blow-dryer first. But, if that doesn't do the trick, (probably not hot enough) then you'll have to get ahold of an electricians heat-gun. The thing they shrink the heat-wrap with.
Now, be very careful with that gun. They do get VERY hot.
Work slowly, a little bit at a time and watch carefully for what is happening. Remember, you only need to melt the surface-abrasion that was created by the sand-paper. You do not want to melt the original texture. Start from a distance far enough to prevent rapid melting of the plastic. I'd say at least a foot away, more if you think it's too hot. Remember, do only a little at a time, until you get more comfortable with the proceedure.
It would probably be a good idea to keep the gun moving "back and forth" a little bit, so as to prevent a strong concetrated flow on a small spot. It can be very easy to over-do it.
Take your time and move-closer or apply the heat longer only in small increases. If this 'plastic-cladding' goes under the truck, anywhere, I would slide under there and experiment under there first, if I were you. You'll want to get a feel for how much heat and for how long "it" will take to react to the heat to get the desired effect.
Now, to tell you the truth, I do not yet own an Avalance but, I have done this with plastic panels on other vehicles and other plastic parts. It almost looks like magic when it changes.
But, be careful, don't over do it.
(I seriously doubt the hair-dryer will work but, give it a try, you never know)
BTW This is the same process used for putting the SHINE on gold-bullion and ingots. Yep! That bright shiny yellow stuff all stacked up in Fort Knox. But, with gold they do use a torch.
I wouldn't recommend that on plastic though. ?
Keep us posted. ?