Here is a late night companion script, _VarPitchHelixExtremes
This script has as inputs the axis length of the desired helix, the instantaneous initial and terminal pitches, and the beginning and ending radii.
Turns is a calculated value.
The math is slightly adjusted from the _VarPitchHelix script.
The math formulas are commented in the script .js file. I should type up my notes on the math.
(The math actually seems to be a bit too easy:-)

There is a verbose checkbox to display the various pitches, and the number of turns.

This script should be perfect to form a transition helix between two helices of the same handedness, same axis, same xy values of start/end,
and a space between them, and different known radii and/or known pitches.

The script has undergone very limited testing, and seems to work well, in alpha status, so use at your own risk.
Entering negative radii or pitches seems harmless, and yields weird or no results, so maybe the parameters should be absolute valued...
There is a crude alert for the two possible cases of division by zero.

(A third script is possible, where Turns is input, and axis Length is calculated.)

- Brian