Alright, a quick update. Today I spoke over the phone (thank you @Heroique for the tip) with the Lee Filters rep. He said and I quote, "nobody knows what size they are, it's a special size and you can get replacements of different screw lengths from BH or other stores".
This brings me back to my original claim that they made it as a custom size so (probably) they don't get their design copied.
I made on the lathe a couple screws in that ballpark, both imperial and ISO and none fit smoothly. Though they were tested for correct fit.
For the brass inserts, the only screw that came close was the imperial 2-56. It goes in nice about 4 turns max, then the brass starts squealing. Luckily there are not many turns in the insert so a steel screw can deform the brass and now you got a standard thread. It's really close but no cigar. An M2 threads in nicely (feels like that's the pitch) but the thread play is a bit too much and I'm sure once you put some load on those threads, it'll slip.
When I have the proper time to experiment with this, I'll cut more screws on the lathe with the size of a 2-56 and different pitches and see what happens.
@Sfroza the major diameter averages at 2.14mm though it's biased towards 2.10mm. The pitch gages didn't give definitive answers unfortunately...
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