Total height of the material within the screws (in my case) is 0.320. That's two layers of the veg tanned leather and the original shoe eyelet, with moderate compression.
3/8 (.375) is too tall and 1/4 (.250) might be too small to get good thread engagement, but I'm going with 1/4 and probably a drop of locktite on each. Plus I'll crank them a bit. But I've also noticed that "1/4" fully closed height can be 5/16 actual, and that would be perfect if it works out that way.
Head diameter scales out at 0.300" (with my actual leather strips scaled against the closeup picture we have) and the ones I found are 9mm (0.354), so that's close enough. Stainless, according to the ad, so I'll spray them white too. Maybe I'll grit-blast the heads lightly so it grips well.
I had considered white plastic (like my D-rings), but I'm concerned about their durability.