Well... Today I finally got around to do my axle swap.
THE GOOD: The new axle is in and the terrible noise has gone away. Fresh mobil 1 syn gear oil. Brakes bled and they work better than they did before.
THE BAD: I don't think the rear axle is aligned properly. On my test drive I noticed the steering wheel was slightly turned to the left on straights. I know I took special care to not move the clamps on the leaves and install the axle exactly where the old one was. I will take some measurements tomorrow to see if I really screwed up, if something is obviously out of line I will try to fix it. If everything looks good but it still tracks funny, should I just pay for a 4 wheel alignment?
And once again. Thank you all for your help. I never could have gotten this far without your knowledge and support.
Everyone loves pictures. So...
U-joint disconnected, drive shaft tied up out of the way.
New gears.
Old axle out. (Note: I put some bigger jack stands in before I started the job, the little crappy ones were terrifying and weren't really tall enough even when they were maxed out).
New axle, lawn chief, wheels, old axle (in order).
New axle up and in.
Almost there.
Old gears. They look like they are in great shape, only a couple specs of metal on magnet over the last 3000 miles. I blame a bearing for my noise.
DONE.