My process is very similar
1. Clean headlight with water or soapy water l
2. Prepare drill pad, and first scor pad 1000p drill speed set to about 8 or 9.
3. Do even storks with the sanding disk back and forth do not stay in one place to long,( could risk scratching.)
4. Rinse with clean water no soap or additives.
5. Move to 1500 pad, do the same as step 3.
6. Now to start polishing with sand paper do it in this order 1000 2000 5000 10000 spending the most time polishing with the 1000 and 2000. (Make sure you keep the surface wet as you polish.)
7. Put wax on a buffing wheel or spare clear and boom. Good as new.
I've done it without the kit, But it is a lot easier with it. This kit comes with everything you need except the drill.