Good news!!!

I called Lutron tech support. I verified my wiring with them, noting that I hooked the hot feed up to the hot terminal that is engraved on the back plastic case, not the hot terminal next to the neutral terminal.
He said the unit is a dual feed, for situations that aren't allowed to have larger than 15A circuits (New York City). In this case the HOT 1 and HOT 2 terminals on both sides need to be connected to hot feeds (or jumpered to the same feed). I hooked my hot feed up to both hot terminals, and it looks like it works now.
You learn something new every day. Hats off to Lutron tech support coming through, on a Sunday afternoon no less.
Multiple hot terminals:


I called Lutron tech support. I verified my wiring with them, noting that I hooked the hot feed up to the hot terminal that is engraved on the back plastic case, not the hot terminal next to the neutral terminal.
He said the unit is a dual feed, for situations that aren't allowed to have larger than 15A circuits (New York City). In this case the HOT 1 and HOT 2 terminals on both sides need to be connected to hot feeds (or jumpered to the same feed). I hooked my hot feed up to both hot terminals, and it looks like it works now.
You learn something new every day. Hats off to Lutron tech support coming through, on a Sunday afternoon no less.
Multiple hot terminals:



















