After spending time going through various Picasa and Google message boards, it seems as if I'm a victim of the recent Picasa migration over to Google+ Photos.
I changed some of the settings on my Picasa/Google albums this afternoon and as a result, the photos in those albums were given new links with my Google profile ID embedded. This of course makes all the old "blogspot" URLs worthless and any photos I've uploaded since roughly mid-February now have new and "improved" Google links.
Unless one of the experts on the Google message boards can help me out, it looks as if I'll be stuck re-building these older posts by re-uploading all photos.
This is an extremely frustrating and deflating feeling. Please don't make the same mistake I did, and leave your old Picasa album settings as is.