I made another design, which fits pretty nicely inside a 4" PVC pipe coupling. The ID is 4.50" and the OD of the ring gear is about 4.625. I think I'll be able to machine that into the PVC. Plastic can be a challenge to machine, so I'll have to see how it goes. Here is this design:
This uses a 20 tooth sun gear, 96 tooth planets, and 214 tooth ring. I will need to see how well everything fits. These gears are only 1/8" wide, so they won't transmit much power. This should have a reduction of about 1+214/20=11.7:1, for 3.66 MPH and 4.15 lb thrust per wheel.
But the same gears are also available in steel, although I'll probably use 16 pitch, which are 1/2" wide. For that, the sun gear will be 12 tooth ($16), the planets will be 30 tooth ($31 each), and the rack will be about $30. So this reduction drive would be about $135.
I'm also thinking about machining my own gears, although mostly for the experience. But gear cutters are highly specialized so you need to know exactly what you want before selecting the cutters. And they're about $30-$60 each.
I want to play around with the planetary drive to see how it might be used as a multi-speed transmission or being capable of shifting in or out as needed, using electromagnetic clutches or other means.