It's definitely the counter balancer.
I took off the stator cover to see if the flywheel was lose and while I was messing with it, I noticed that the counter balancer wasn't turning in concert with the flywheel. I haven't taken off the clutch cover to check out exactly what it is because I'm dreading messing with it, but I'm about 99% sure something is slipping. Sometimes the counter balancer will catch and do what it's supposed to do, occasionally it'll slip.
I really don't feel like taking the clutch-side apart. What a bummer.