Originally Posted by danlrc

Note: the Tam gearbox ratio, not including the motor pinion (10 tooth) is 600:1.

So all this 4:1 and 3:1 nomenclature really lends confusion, since the gearbox ratios are actually up in the 600:1 range.
The 3 and 4 shaft count description is one way to generally describe gearboxes, but it's the number of gears on each shaft and their tooth-count that determines gear ratio, not just the shaft count.
So neither method, shaft count metod or 3:1/4:1 method, are accurate ways to describe the actual gearbox ratios.
I can provide example calculations if wanted.