The stuttering has mysteriously gone away today. No idea why, if anything, I've added stuff to my game since yesterday, so it looks like it's nothing to do with C2 but something to do with my PC.
To Tokimson, I found that a blank project ran at a steady 60fps. I tested it yesterday while my game was stuttering, but it ran at 60fps and never changed. So I dunno what's causing that on yours.