I did copy the CONTENTS folder and "last clip" from BluRay to a SATA drive. At first, it didn't work - same issues as BluRay. Then, I downloaded Roxio Creator 2011 (updated for Windows 7.) I didn't think this would make a difference since I had been able to perfectly read and import Quicktime media on BluRay. But it DID make a difference (although I still don't know why!!)
So, now, I able to read and import the P2 media from the SATA drive - and I know that the data on the BluRay isn't corrupt. So that's good!!
Today's experiment: Burn the p2 media back onto a BluRay -- but this time, I'll put the CONTENTS folder and "last clip" into it's own folder, instead of burning them directly onto BluRay. I'm told that this might fix the problem.