I saw your tag on the end of my post asking the same thing, here's what I discovered.
I had about 3 coats of BB/CC and a primer ON TOP of my original paint and when I sand blasted I took off everything down to the plastic on one side but shifted to just talking off down to the original paint or primer once I had the pressure and feed rate (thanks to Shine) adjusted.
When I hit it with two coats of black epoxy it didn't seem to care which was what. I did my repair on top of the epoxy (3M 0801 panel adhesive) and just covered it first with the reduced epoxy as sealer before paint.
That's how I did it but *I* am just a novice and my bumper cover was more a guinea pig than a project.
If your just working with the original paint I'd guess you don't have to strip it all, maybe just the clear coat off???
Try to get the sanding pad off your sander and use it to hand sand in X pattern starting with some 150 if your 220 doesn't cut enough and then working finer. I find the the round shape helps get in some of those tight places.