Okay, after a LONG, exhaustive search, I'm going to answer my own question in case future archeologists stumble across this lonely thread. We settled on a support ticket system called Trellis Desk. Of all the free/low-cost PHP/Perl packages we tried (many), this was by far the best. Seriously, nothing else even approaches it, in terms of flexibility, themeability, admin power and interface, etc, etc. So I definitely recommend checking it out. The only downside is that the community support forums are down indefinitely, but the makers (Accord5) seem to still be alive and kicking, so I'm hoping the support forums come back online. I'm only having one technical problem, which is that notices of tickets submitted by email (yes, it pipes them perfectly) are not being sent along to all the appropriate staff. That's a minor issue right now, though. Everything else is smooth.

http://www.accord5.com/trellis