Good morning Jed --- what's left of it...
I looked at your pictures, I don't see anything glaring at me in regard to the install of the basket drive on the gearcase, and I looked at the centerpost inside pics too.
It looks like you may have some rust developing inside the centerpost, but some of the grease WP used was reddish orange, so that stuff immediately above be bearing may be grease, I can't say for sure. You may be wise to replace the centerpost seal at the very top, that is a large part of what allows water into the centerpost, that and the spin tube seal.
Your spin tube is not damaged or corroded, which is great. Clean it well and re-lube it, it looks VERY dry, as do the bearings. Drop about a teaspoon of turbine oil above each bearing, and put more on the bearing surfaces and liberally all over the spin tube (once you clean it). Oil the bearings with the machine on its side and don't upright it until the spin tube is in or the oil will run out.
In pic number 31, that circular spot is the braking surface for the brake pad to rub against. The brake pad is on the top of the basket drive. Clean both well and you'll have a more effective brake. Don't be surprised if when you finally have the machine running properly, that you hear a bit of grit during the braking process. This happens sometimes after "major surgery". Little grains of dirt leftover from all the work amplify themselves seemingly 1000 times when they're in between the brake components, and you hear it all over the machine. They work themselves out eventually.
The reason the machine spins with the gearcase loose is because the basket drive parts are tightly gripping each other until the final few turns of the trans bolts. These last few turns do the same thing as pushing in a car clutch pedal. This last distance is what brings the clutch pads off the pulley surface. It will also engage the brake.
Al brings up an interesting point --- the spacer should have fallen out as soon as you removed the lowest of the three gearcase bolts. It often makes a racket on the cabinet when that bolt comes out. Out of curiosity, how many unused parts do you have left? If you haven't been using the spacer on the short leg of the three gearcase mounting rods, chances are very good that you'll have the gearcase in a major bind. The short one of the three is the one facing the front of the cabinet. Put the spacer in the gap between the transmission and the mounting stud, and thread the bolt though the gearcase hole and the spacer. It should properly tighten together.
Let us know what's next Jed!
Gordon