The 12-32 is sufficient model identification. However as you say, the only information that seems to be available is the parts diagram which does not give much idea how to remove and reinstall the broken shaft. I did notice from the parts diagram that it is called a square shaft because a short section in the middle of it is square, to engage the square holes in the centers of the drive plates.
There seem to be two drive plates, driven by two pulleys, each with a clutch. There is a small sprocket on one end of the shaft, chain-driving a huge sprocket on the rear axle. From the totally inadequate information in Illustration 5, I suspect you need to remove the two bolts holding each of the flanged plates at opposite ends of the axle to side members of the chassis, then you lift out the axle complete with bearings/pulleys/clutches/drive plates, sliding it axially off the belts as you lift it. Then with that complete axle system on the bench, you transfer the parts one by one onto the replacement axle. Note there is a nut on each side of the pair of pulleys/clutches/drive plates. You will have to remove a nut to slide the square section of the shaft out of the pulleys/clutches/drive plates. If you keep Illustration 5 handy, and memorise or photograph each part of the original assembly, you should be able to do all this fairly easily if it works the way I've guessed. Some photographs of the ends and middle of the shaft on your mower, taken from directly above, would help clarify this.
I've looked at the Greenfield site and it was completely unhelpful. I've read elsewhere that if you contact Greenfield they will give you the parts list that is available on this site, but that is all they will give you.
