Sorry to keep posting, but I'm just going to update this thread in case someone comes across it later and finds it useful.
I got my biometrics and interview appointments for Sept. 18-19.
What I was doing wrong originally was putting "Sept 4" -- the first date of availability -- in the embassy interview box. Because that date was so early, there were no biometrics appointments available.
When I changed the interview date to the third week of September, that's when a bunch of biometrics appointments became available in the second box.
This may be self-evident, but it was confusing for me, so I leave that here in case someone else was having a similar issue.