Looks like “Healthy San Francisco” is just another name for it / they’re consolidating similar services, because the place that I made an appointment for today is part of the sfccc.org thing. http://www.sfccc.org/sfcccclinics/mnhc.htm
( there’s a dropdown list of clinics in “healthy san francisco” here: http://www.healthysanfrancisco.org/visitors/How_To_Apply.aspx )
I guess I could try calling all the ones on that list to see if there are any that have appointments earlier. Thanks for the resource, though, I hadn’t come across that site yet.