I just read through the thread, very nice work @Jeff Siddall ! Being a software engineer by trade, working mostly in python, I really appreciate the work you did here! And twisting the fretboard is a whole new level there...
Going back to basics, I understand that having a straight fretboard under each string means that the fretboard will be a slice of cone where the top and bottom radiuses depend on the string spacing at the nut and bridge, on top of the base radius you choose at the nut, right?
My intuition tells me that this works also if the strings are not regularly spaced, when the e and a strings are farther apart than d and g, is this correct?
Another thought I had was that I usually lower the frets a nudge on the bridge end of the fretboard, so I'm wondering if the curved fretboard path can also be desirable. By computing the hyperbola equations (in other words, staying with conic maths), one could maybe make a fretboard with a custom fall-off...
Thanks!
Regarding the string spacing, yes, it doesn't matter where any string goes as long as it is along a path defined by a ratio of the string spacing at the nut and bridge relative to the centerline.
So, for example, you can put a string at 10% of the distance from the centerline to the outside string at both the nut and bridge and it will still be on a flat string path. You can't mix and match though. For example putting a string at 10% of the distance at the nut but 20% at the bridge will result in a non-linear string path.
Regarding fallaway, yes, theoretically you could cut a longitudinally curved fretboard in addition to the typical transverse curve. However, the fretboard will naturally form a parabolic shape under string tension so I don't think there is any benefit to cutting that into the board itself.
Using conical segments won't provide a fallaway since a cone, by definition, is a ruled surface.