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How certain are you about that 6.25 degrees? Or I should say, I am curious how you derived at that.
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I got it from a german WW2 Periscope Manual
The scale there was 10/16 of a degree per mark, and the "100" mark was 6.25 degrees and the example showed a ship at 250 metres. So I investigated a bit why that figure was chosen and soon understood that because tan 6.25 = 0,10 it made sense to get range figures. Actually, 5.75 degrees would be evn more accurat but apparently the rest of the scale wouldn't then be evenly distributed.
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When looking at your sketch-a-scope  the thought popped up in my mind that the 10 might actually mean 1/10 radians, which is equal to 5.729577951 degrees (0.1*180/pi; and not too far off from your number, but in the ball-park if the SH3 scale is indeed off) If you are not familiar with a 'radian' (though I'm sure you know), it is the angle you get when the radius of a circle is wrapped around that circle. The tangent of one 10th radian is 0.100334672. So if according to your picture the distance E1=Mastheight*10, it could be rewritten the same as as Distance/Mastheight= 1/tangent(radian/10)= 1/ 0.100334672= 9.966644423.
If a contact measures up to be halve-way the 10-mark (and waterline) it is actually 1/20 of a radian, and again halve-way from that 1/40 of a radian. And with those numbers it rounds nicely to 20 and 40 also. The appearant linearity of the telemeter scale puzzles me though. It's not convenient for those 20, 40 numbers.
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Actually, the sketch was done in an attempt to make it useful for SH3, therefore I kept the current subdivisions and wanted simply to modify the field of view of the periscope to ensure that the "10" mark matches 6.25 degrees and not 10 degrees.
But the historic periscope reticle looked like this one here (Please see if the subdivisions used make sense for you, your expertise in maths can probably provide a better solution
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Picture of a real scope (Note that sometimes there seem to be three marks in the same space where there are four on the opposite side of the central cross):
