Turntable dust cover cleaning

Novus plastic polishing kit. As @mijostyn said, work in straight lines. I don’t know if you will get them out, but you may be able to make them somewhat less visible. After that, just dust with a swiffer. If you can’t get anywhere with the Novus, buy a new one and just dust with a swiffer. 

Novus #1 is great.  It's supposed to have antistatic properties, so it may work for you.  If the cover is scratched, try #2 or #3 and then #1.

Everyone

OP is not talking about scratches, just streaks, static and dust

"Pretty much every day, I have to clean streaks off the cover. There is a very high amount of static."

Nasty Scratches

I made a terrible mess out of a dust cover which was under something else I was working on. STUPID!

. I took it to my auto body shop. They got it down to the point where I could perfect it with the Nova 3 step kit

https://www.amazon.com/Plastic-Acrylic-Scratch-Remover-Starter/dp/B07C45XV6W/ref=sr_1_5?crid=3AWYVHRDHKJRO&keywords=nova+3+step+scratch+remover&qid=1698599239&s=hpc&sprefix=nova+3+step+scratch+remover%2Chpc%2C61&sr=1-5

They also can buff up old cloudy plastic headlight covers on cars, big differences: amount of light and appearance

Seems to me that whatever you are using to "clean" is the cause of the residue in the photo. I have used Sprayway myself for windows and it is far from streak-free. You might get better results with a mild solution of distilled water and white vinegar.

For windows, I spray the window and then buff it dry with newsprint (yes, newsprint), but for the turntable cover I would use a soft, liny free cloth like one used to clean computer screens.

Not sure why all the talk about swirls, when that isn't the issue.