And i really appreciate you reading my walls of text 😄
Current helical gear add-in UI for context (this one already as the dendum multipliers exposed which my released version does not)

Given the UI limitations I was thinking of breaking the gear into standard sections and allow the user to control each section of gear generation (eg: a double helix would have: cap, face, point, face, cap - where the 2 faces would be treated the same but of opposite helix directions but the 2 caps might be treated separately).
Along with the standard inputs of helix angle, pressure angle, teeth, module, backlash, handedness and "thickness" I plan to also surface addendum and whole depth multipliers as an advanced option and adding double helix normal and double helix radial standards. Then give control over the endcaps and point transitions (for double helix). I was thinking of providing a canned list of options (e.g. dropdown) for each with appropriate icons of course.
For end caps I was thinking of the options of:
End Cap Style: None, Parabolic - ease out, Parabolic - ease in, Parabolic - ease both, Linear Taper
End Cap Position: Outside, Inside, On Center (relative to the specified overall thickness of the gear).
And a checkbox to give the option to leave the end "pinched" or to restore it to the root cylinder.
I could either provide a few canned values for the various options or give the user a set of dynamic inputs (ok so hidden or shown because dynamic is not really practical) to give the user more control over the radius of the small end of the cap and how thick the cap is. The issue with this is that it is most practical to specify radius as relative to the outside, pitch, or root circles and to specify both radius and thickness in units of module or whole depth is even better. Using whole depth would mean that the user could change any other gear param and the end cap would still "look", and more importantly, print the same without having to futz with the values specified.
Similarly the transition point between the two halves of a double helix gear has a load of options
Transition Style: Sharp, Strait Segment, Smooth, Cosine, Parabolic, Smooth to Strait, Cosine to Strait, Parabolic to Strait
each of these, except sharp, has a length involved - and the XX to Strait options have 2 lengths, the transitional length and the strait segment length
Then there's also the option of reducing the radius through the transition as well to avoid point loading (and lets face it that point gets messed up when 3D printing)
... and we haven't even gotten to the exotics like those wavy gears - those would likely be fully canned options, or perhaps I could let the user specify the number of direction changes at least.