I like the concept a great deal.
This is merely how I'd construct something similar based upon the concept.
Keeping the circles all the same and the bars the same width, and then remaining consistent with the width of the breaks is what I would aim for.
I might play with the angle for the 3 a bit. I tried a 45° triangle and that was too great an angle in my perception. And I tried a leaving the cuts in the "3" at the 0° angle - both those options seemed to be promoting the appearance of a "e" more than a "3". But there may be something between 45° and 0° that works better than the 60° which I used above.
As 0° cuts.. I guess you'd have to decide whether this shows a "3" or an "e".
Playing a bit more.. bringing in the bar of the 3 so it is offset by the same 15pts from the edges of the inner arc cuts seems to promote a 3 more to me. I also squared off the cap of the 3 bar, to match the square cap of the tail on the p and the a.
Then I realized I could possibly align the bar at a 60° angle from the inner points on the arc cuts.. So I tried that.
From here, I've got about 4 subtly different variations. I'd create a png of each.. wait a day or two.. then come back and look at them with fresh eyes to allow me to choose which direction I felt best conveyed the 3. And then adjust
further if needed.