Best deep-scratch repair kit/system?

Wet sanding followed by compound followed by polish.

Do you have pictures?

I'm sure others will want to see a picture to make the best recommendation based on the scratches.
 
I think AGO has something. However, 2500 grit sand paper and 3000 grit sandpaper Meg's Wet sanding block. All wet sanding of course. You can youtube on how to. It is real easy once you know how to do it. It is also good with headlight covers too. Make sure afterwards you have a compound polish and a finishing polish.

DA orange pad and white pad. Check AGO I think they have a Megs kit or some others too.

If your fingernails get caught in the scratches it will be too deep to completely repair. You can fix quite a bit but it will need touch up paint.
 
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