Search API Attachments not working
Ok, this looks like part of this is a case of PEBKAC. Or maybe could be considered an issue of documentation.

It looks like the default search box form does not interface with search API and that in order for the search API indeces to be used you must use the Search API Pages module. 

However, re-indexing definitely does NOT re-index attachments on existing nodes. I'm not sure whether it's supposed to or not but that is what threw me to believe it was not working.