Checker, I don't know if it will do, but there's a Slingy strap on Ebay right now..... item number 310172462017
Thanks Kevin, it looks like the exact part, and in fact the listing refers to it as a Slingerland/Ludwig/Rogers replacement part, so I got one.
Now...anyone have a pic of the bottom of the pedal that shows the screw that goes through the leather strap? I just realized I'm missing that too. I can probably pick one up at a hardware store, but I'd like to see what it looks like, if it has a large washer, etc.
Scott