As part of my techno-wrangle yesterday I beat on my router for a portion of the afternoon. It appears that the dropped-connections issue I was experiencing was indeed the result of a badly-configured router. Thanks so much to the inattentive support staff at my ISP!
To be fair, I’m their client because of legacy ISP purchases and they are really not set up to support residential DSL. Still the problem of the misconfigured router came about because they’d failed to rebuild the network interface once Qwest had reset their fiddly bits. Amusingly, Qwest’s forwarded support number for my account goes to the old ISP’s former CTO’s voicemail box.
At any rate it’s a relief to have stable connections again.