Thanks for the help!
But, yeah, we didn't do that, either.
We ended up removing the second smart list, because that was seemingly the only way to send our campaign. So now, while it says that it's been delivered to 235 leads, there are still 0 leads that show up in the results page. Very odd...
I thought I remembered seeing a button to refresh and sync up with SalesForce, but can't find it now.