When I worked in the jewelry repair business, we used Novus plastic polish on soft things like plastics, acrylic and even amber jewelry!
It comes in three types, the #1 is the finest but we used the #2 (red label) for everything we did at our shop.
https://www.novuspolish.com#2 is for fine scratches - I see someone on the Novus website used it to fix his nearly new camera's LCD screen and he was really happy.
For very heavy scratches, they have #3. I never used that but it might be great for motorcycle or boat windshields? I think #3 needs to be finished with#2 afterwards, as it is a heavier abrasive.
It's a liquidy paste, you will probably need only about 10-20 DROPS on a paper towel to fix your screen, maybe 1/4 teaspoon? Rub in small random circular motion for a few moments and check your work. Repeat until it looks amazing, it doesn't take long.
Try not to get it in the edges of the control buttons or off the edge of the screen as it might get trapped there and it's kinda brownish.
from the SDS (safety data sheet)
Skin Irritation Category 2
Eye Irritation Category 2A Skin Sensitizer, Category 1B
GHS LABEL ELEMENTS:
Signal Word: Warning
Hazard Statements:
H315: Causes skin irritation.
H319: Causes serious eye irritation.
H317: May cause an allergic skin reaction.
Precautionary Statements: Prevention:
P261: Avoid breathing vapors/spray.
P264: Wash thoroughly after handling.
P272: Contaminated clothing must not be allowed out of the workplace.
P280: Wear protective gloves and eye protection.