I'll check to see if it's possible for the search to work correctly using a GET method instead of POST. My understanding is that if I want to pass form fields back and forth between pages, I need to do so via the POST method.
In any event, I've been able to go back to the previous page and all of my criteria are still intact. Maybe I need to see how long I can get away with sitting on the results page before that's no longer true. Also, it's likely I can specify that a particular page is cacheable for an hour or something like that.
Since this is a strictly dynamic-content site (all pages are the product of realtime queries to a contantly-changing database), I've got everything set to expire immediately.