This same situation (slow slow response time) has happened at least three other times in my 3+ years on this site. Each of those times it did take some time for someone to actually do and/or change something fundamental (new server, new hosting software, etc) to improve the site's basic performance. So whether it's the continued growth of the site or something else, the site does seem to need some careful care and feeding again as it has needed in the past.
Thanks for any help that can improve things here.
Lefty