[JessR]

Go buy the the hub adapters - they are available from any Power Wheels dealer for $5 or less each.
The hub and transmission hole are about 7/16 dia. as I recall.
Drill it out to 1/2 inch and use a 1/2 inch shaft (aluminum is good)

To mount the transmission, locate it by mounting the shaft on two bearings or bushings, and use it as a torque arm transmission - the gearbox floats on the shaft, just keep the box from rotating. (you can for instance make a small plywood "box" that just accepts the gearbox, with cutout for motor, or just a single sheet that outlines the shape of the box).
You can drive a drum off the adapter, a sprocket, or drive a cam.
As you probably know, use it in applications where it will keep rotating and cool. Dont use the FP where it will stall often, the small motor will let out the magic smoke pretty quickly.
Good luck.