Soooo, decided to try something completely different. Signed up with OpenDNS yesterday around 1:00pm. It has been over 24 hours now, and I haven't had to reboot the DSL modem, and pages are still loading fine.
In a nutshell, the problem didn't seem to be in the filters or the phone splitter, the problem resides in Bayou Internets DNS servers, since using OpenDNS isn't giving me any problems.