I have still been thinking about this whole planetary design question and realised there is another option for a gearset that we hadn't tried. Fraction Ratios.
I was able come up with the following:
Here is Oldbelt's gearbox fitted with 1.25M 25°PA gears in the following configurations
Gearset 1 (Sun, planet, ring): 12-15-42 gives a ratio of 3.5 plus the 1 for the carrier output = 4.5:1
Gearset 2 12-16-44 gives a ratio of 3.2/3 plus the 1 for the carrier output = 4.2/3:1
4.5 x 4.2/3 = 21:1
It could probably also be done with 1M 18-63 and 18-66 sets and the appropriate planetary gears but the housing would have to be 10mm larger in diameter.
I was asked, "Are these gears too big for the desired motor to drive?" I have no idea. Does anyone know how to calculate this? (we overhaul gearboxes, not design them.)
I notched the output shaft, added gear constraints and a handle and turned it 10.5 times. The output shaft did 1/2 a rotation. I was happy!