More on the problem:

Sure, the session cache is the same as my browser cache, since when I empty
the browser cache the problem disappears -- until yet another session is
started. The /tmp/sess........ file shows the correct $count value for the
current session, but during that session the browser pulls a previous page
version from cache with an old $count value (stored nowhere but in the
pages in cache, from what I can see).

Man, this is frustrating. Please help.