Probably calipers will work ok. If you can straddle the thread from the end, then you can kind of pinch the calipers shut over top of the wires until all three are captured, then take the reading. There is a little calculation sheet that comes with the wires that tells you how to calculate the pitch diameter from your measurement. Don't lose that sheet, in fact, laminate it to protect it
The method I recommend for threading is not to try to calculate it to extreme precision in advance. You need ball park figures to work with, and you need to know what "almost done" should look like. That is what the crest width information is all about, because you do not actually measure the crest widths with any precision, but razor sharp is a sure sign that the thread depth is overcut.
For external threading, I deliberately cushion the tool offset so that I know the thread will not be overcut in depth. PeeDee it with the wires and figure out how much further to go. Then either adjust the tool offset or the program to hit the correct size.
Same logic with the ID thread: you know the toolpoint represents a small cross section of the male thread. So the logical X endpoint for the internal thread is going to be .001 to .005 greater than the major thread diameter. So trial cut the first round of passes on the ID, stopping the tool exactly on the major OD at the last cut, and try the gauge. If it is too tight, then adjust the program endpoint or the X offset by .002 and run it again.
Be prepared to sacrifice the first sample nut that you make until you get this down pat. Don't spoil a part that has a whole lot of time put into it already.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)