I eventually figured that it was probably something to do with the animation, so after poking around characters\_male\idlanims a bit, I came across the "chair_backenter.kf". Since it was present in my data folder, I assumed it was added by a mod. After checking the Oblivion - Meshes.bsa and TES4Edit, I determined that there is a Vanilla version. So what I did was create a BAIN project pointing to that mesh and see what mod conflicted.
Consider my surprise when I discovered that there was no conflict at all! As far as I can remember, every portion of this Oblivion install, with two lone exceptions, Sensual Walks Animations and DarkUI Darn, was installed via BAIN. I've gone ahead and unpacked the Sensual Walks OMOD and confirmed that it doesn't touch that file at all.
Anyway, I went ahead and deleted the file, loaded the game back up, and unsurprisingly, the problem was fixed.
Does anyone know of a mod that Adds the various chiar animations? Because I've checked the likely culprits (Real High Heels, Dynamic Foot Position [which was deactivated anyway]) and I couldn't find a thing.
So just throwing this out there to see if anyone remembers something off the top of their heads.