Thanks everybody for your help. We upgraded our postgres to the most recent version and reloaded the database, and have seen a huge performance increase. Our moodle installation is running better now than ever. September is typically our busiest month, and with over 16,000 users we haven't had a single complaint about performance.
We clustered a number of our high-use tables/indexes, and will probably recluster every few weeks.
We also implemented a number of postgres tuning changes which may or may not have helped, but they certainly didn't hurt. Here are the notable settings that everyone seems to talk about when it comes to performance, and how we have them set on our server with 8GIG RAM.
Thanks again, -- john