OK, latest update: Photobucket works well, but I'm still having trouble with albums and organizing.

But, I found the app PixelPipes that has successfully allowed me to upload a photo to Picasa, even specifying the album! (Except, I have to know the exact name of the album or it will just create a new one. But I'll consider that a minor annoyance for now.)

The problem is the app is reeeeeeeeally slow. It's so slow that I swear it's crashed or didn't register a click, so I click something again, which actually does half crash it (not responding box shows up, but if I click wait it's usually fine).

I don't know whether this is a setting that can be changed, but also if I specify a new (non-existing) album name at the point of upload, the album is created as private. The problem here is that if I can't edit my albums online to make a private one public, then I can't use the edge to make this photo viewable, although I can get it into Picasa and into an album. I'll have to try that next.