You could get all that out, probably, with effort.
It might make the plastic of the screen really thin though - to remove a scratch you either need to fill the scratch in, or remove all the material around it to make it flat again. Filling is more miss than hit on transparent plastic.
A set of polishing compounds would do it - like you get in a headlight polishing kit.
Problem is, if you don't have the stuff already a new kit is likely to cost more than a new mod anyway, and if you've never done it before you're likely to wear straight through or melt it...