Dunno how you got on with this, but fresh in my mind after detailing my daily driver recently.
For deeper scratches, polishing by hand means you can be much more precise about where you apply pressure, and how much. You are removing clearcoat/paint, and it is better in my view to remove only as much as you need to.
Work on the scratch using something like ScratchX or if you need a bit more cut, Meguiars Ultimate Compound. Neither are too aggressive that you will cause damage quickly. Expect to work on it for a while, be patient and check how you are getting on regularly.
You will be able to produce pressure through your fingertips more precisely than you can with a DA.
But worth using a DA for general polishing... I use Chemical Guys VSS for freshening up swirled paint- works well, but does not make much impression on deeper scratches.