OK, well I guess something went screwy with my settings or something, because when I played this afternoon it was no better than ever, and when I loaded it up just then it was much better. Maybe the patch reset the default graphical settings or something, and when I opened the menu this time they went back to how I had them set. Performance is still not good, but as long as I keep every setting as low as it can go (the only luxury I've allowed myself is 16xAF) it no longer stutters (much). I think I could probably lock it at a stable 30FPS now, with only occasional stuttering.
If I even think about raising any setting even to Medium it's back to stutter city, though, and JC3 on Low settings at 30FPS is definitely an uglier game than JC2 maxed out at 60FPS. I suppose I'll come back after my next GPU upgrade.