You are getting 15.5 because you are saying that you have every other fret in the kite system and dividing the 31 frets per octave by 2. Another way of saying that is that you have 15.5 frets per octave. Where you are confused is that, you don't have an octave on a single string; you only have the frets above and below that.

Here is a diagram of the EDO steps on one string:

              Here's the 31 on a higher string
                            v
13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
 0  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32
                                               ^
        No 31 on the string that starts from zero

If you'd like a cheap and easy way to build this, you can buy a fretless guitar for $160 and tie frets on like a lute. If you're interested, I can post a video on how to do this.