No....it's all this imbecilic mention of cIPL flashing that's scrambling my brains. Never go near the cIPL with your PSP. The reason you have a perm firmware is nothing to do with a cIPL, it's because you have a 6.20 nightly which has the modified vsh prx rendering it permanent. Therefore all you need do is to get the 6.20 B10, run the permanent patch (not the cIPL flash) and uninstall it, then PROUPDATER to uninstall the Nightly and then run it again to install the files for PRO B10. Personally i'd leave it as a temp fw but at that point you can use the perm hack which is safe for your motherboard (NOT a cIPL).
In short, you're on 6.20. Uninstall the Perm patch, uninstall the Nightly using the 6.20 PROUPDATER and then Install PROB10.
NOTE - there is a small chance of a brick if you uninstall the perm patch. If you want the safest option just update to 6.60 OFW and either use 6.60 PRO as a temp CFW or downgrade back to 6.20 afterwards.