I'm pretty sure it's all JIS. It's a 1995 Motiv mountain bike. I don't know a whole lot about the Motiv brand, other than I have two of these '95 Stonegrinders, and they seem nearly bomb-proof. They seem like an Asian-based builder/reseller.

The outer diameter of the cups are 30.0mm and the inside diameter of the frame tube is about 29.9mm. The outer diameter of the crown race seat on the steerer is 27.1mm and the inside diameter of the crown race is 27.0mm. This is all on the old stuff. My Tange fork also has the 27.1mm crown race seat.

So it looks like I'm looking for a 1" JIS threadless headset. These seem to be difficult to find (I don't see much on the internet). I will go back to the bike shop tomorrow, though, and see what standard their set is. If ISO, I'll know to move on (and I'm pretty sure it is).

Edit: And, actually, now that I've learned what I have (thank you!), I think I'll just modify the top race by removing the threads and finding a compression washer that'll work. That should be as good as any headset that I can buy (and much cheaper). And if I decide I want to go back to threaded, I haven't ruined anything that I can't replace -- threaded headsets are 5-10 bucks online all day long.