I just spent 45 minutes on the phone with a support tech and we were unable to resolve this issue, so I was directed to try posting about it here while my support ticket is bumped up the line to the network folks.
In a nutshell: I'm experiencing stability issues of some kind on my line, but only when I have an IP in a range other than 70.x.x.x. While general browsing works fine, there are definitely connectivity issues present, as a persistent IRC client connection I run on my home server cycles its connections every 5-10 minutes (resulting in a barrage of connection information pings), and I notice short drops in AIM/GChat connectivity as well. This only occurs on ranges other than 70.x.x.x; recently, I've been receiving IPs in the 173.228.x.x and 50.0.x.x ranges instead.
This has actually been an issue for a long time (I've noticed it whenever my IP changed to something outside 70.x.x.x), but in the past I'd always been able to cycle my modem and receive an IP in the latter range, which has fixes the stability issues. I'm aware that it's strange that a different IP range would cause this, but it's really the only thing I can definitively link to the issues I'm experiencing. Nothing else in my home setup has changed, and this only really became an issue when I recently was unable to reacquire an address in the "working" range.
My current IP is 188.8.131.52. I'd be glad to offer any other information as needed. Thanks for any help!