It was really very simple in the end: Uninstalling Creative's bad drivers and using Windows' default high definition audio device driver fixed the stuttering completely. I could reproduce this every time I tried.
As for why only Nestopia seems to suffer from this, I'm not really sure and c0d3h4x0r hasn't ventured any guess so far. I thought it may be the DSBCAPS_GETCURRENTPOSITION2 flag in NstDirectSound.cpp, as I've read that the GetCurrentPosition implementation in Creative's shitty drivers messes up the hardware buffers, but I'm really very much out of my league here and this is something c0d3h4x0r would have to investigate. He doesn't seem to have a Creative card and couldn't reproduce the problem in the first place, so I'm not sure if he'd be successful.
By the way, FirebrandX also demonstrated that due to ATI's cards being underclocked by their drivers too much in 2D mode, this can also manifest as unstable VSYNCing and thus be followed by sound stuttering. If you've already edited your CCC profile to rectify this and the Creative card was still the culprit, well, that only adds to the evidence against Creative's drivers.
Their drivers are a buggy, bloated mess which barely works adequately, and yet over there no one seems to care. I understand they've been going through rough financial times (they're slowly becoming obsolete thanks to integrated chips) and might not have had as much to spend on driver development, but the state they've left them in is in disarray. Their forums are filled with complaints regarding that.