No. It's the regular SMB 1-3 and Lost Levels version.
I did. Just a few minutes ago a cleaned it again. I got a little more dirt out, but it still won't behave. Then I remembered that I had a Game Genie lying around, so I tried running it through that.
Oddly, it does work connected through a Game Genie. I hadn't thought to try that previously. So I guess that's one problem solved. It makes me wonder if perhaps All-Stars would work when connected to a Super Game Genie, but I don't have one of those.