Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
Please see my response about changing reference frames above. It does not "lack".
You can't reference your claimed matrix calculations or any curvature calculations. I understand.
You didn't ask.
Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
I understand the matrixes busywork that may be completely ignored in operation.
https://image1.slideserve.com/1902429/transformation-matrix-continue1-l.jpg