Okay, I had some extra time today and was a bit more patient with my research -- and I found a way to upload photos again.
The following is for my fellow Bloggers who are having the same problem and have not discovered this solution yet:
At the top of the post editor page are several tabs, one of which is Settings. Select that, and toward the bottom, find Global Setting, and select Old Editor (be sure to Save Settings). Voila, and we can happily upload photos again!
Blogger should really make this information a little bit easier to find.