STOP EVERYTHING! I really don't thing anything you do by hand from here on in is going to get you where you need to be. Here's what I'd do:
#1) Do you have or know anyone that has a rotory or at the very least a Random Orbital (aka PC) Buffer?
#2) If yes, do they or you know how to use either? If no, find a professional and cut your losses.
#3) If yes, see if you can get by with a light compound and the Random Orbital with fairly aggressive pad (Yellow or Orange and I still don't think this will get it but then again, I haven't seen a pic.) Then work your way up to a heavy compound if the light/ medium compounds do not get you the results you desire. If after all that, and the Heavy compound and the Random Orbital don't get you where you want, and you are, or know someone who is proficient with the rotory, start with a medium polish and follow the same routine. (I wouldn't spin the Rotory at any more than about 1200 rpm with an 7"-8" pad) DO NOT LET THE PAINT GET TOO HOT!!! I CAN'T STRESS THIS ENOUGH. Work slowly but keep the buffer moving. Just go ahead an do a 2'x2' area. You're going to have to protect the whole panel in the end anyway.
#4) If you've had get into compounds (And I DO NOT MEAN ANY TURTLE WAX IN A RED OR GREEN JAR), you'll HAVE to then take it a second step and polish
it. (Do the whole panel with the polish so you've got some uniformity.)
#5) Add a sealant or good wax to the masterpiece you've just created, sit back and call yourself a wizard.
If at any point you are unsure of what you are doing, Stop! It's not worth damaging beyond someone else's repair if you're not absolutlely certain you are correcting the paint.
Hope this helps a bit. Don't hesitate to contact Walter or myself via PM if you have any more questions. Best of luck to you.
Jason Boyer
Co-Owner/ Tech. Advisor
Wet Werks Auto Salon