Refurbishment of a turntable lid

[OBELIX]

Hi all
I have obtained a turntable with a plexiglass lid which needs som attention and refurbishment.
I know NOT TO USE any ammonia based or the usual kitchen cleaners......Any ideas how to remove dull patches and small scratches and get back the clarity and shine ?
Thank you

 

[Shonver]

 

[marantz123]