On an english threaded steer tube that has been filed to a smaller od on the shoulder.
Owner says the shoulder is 1.0698 ± 0.0010 inches.

If you are saying that the fork crown race sits loosely on the steerer tube's fork crown and is not a tight press fit, then one method to make the fork crown race sit tighter is to use a punch all around the steerer tube where the fork crown is supposed to fit tightly, which will dimple up some metal to grab onto the fork crown race and make for a tighter fit

No, there is no fork crown race. I would need to buy a headset assembly, hopefully with a race with a smaller ID.

ISO crown race ID is 26.4mm = 1.039"
JIS crown race ID is 27.0mm = 1.063"

So pick one.

I agree. The alternative I would choose is to take the fork to a well-equipped shop and have the fork crown race seat machined down to fit an ISO crown race. You'll just have to remember that you have a hybrid headset, though, unless you have the headtube reamed and faced for an ISO headset.

Good cheat sheet: https://www.sheldonbrown.com/cribsheet-headsets.html

So he's filed it "down" so that it's still larger than JIS? I think you need your own calipers - don't trust him. And if it is larger than ISO, and the head tube is ISO, I'd have your LBS cut it down to ISO size. With the right Park tool (and others, I'm sure) it's really an easy job.