You’ll never really get the black swirl marks out of your playfield without using a magic eraser and some alcohol, but in doing so, you strip off the playfield protective lacquer coating—leaving the ink bare and prone to future exacerbated wear.
It looks like you’ve got a fair bit of planking though too.
If it were my game, I’d probably just gently clean with a rag and naphtha, then wax with a nice durable carnauba wax. Don’t stress over imperfections. These games were meant to be played.