Kevin
A couple things I noticed in your photos.
This has to be 55 machine that is the older style door boot, they changed the opening in 56 on all the machines. The boots I have fit the later style. The only modern boot that fits this is the small door Speed Queen so I'd get one of those on hand pronto. Also I'd start rubbing that door boot down with glycerin on both sides of the boot, it just might bring it back. You can get that at any Drugstore.
Also on the motor, you say it buzzes, these machines used the notorious Delco motors and they have the same problem as Frigidiare's, the start switch sticks, doesnt' cut out and burns the windings by over heating. I'd lube the front motor bearing there should be a lube hole drilled in the top of the shaft behind the pump. If you have one of those pin lube tubes you can get it in there, you might even get to lube the shaft of the start switch. Robert had an article on this switch here many many moons ago. Once the start switch is moving then I'd run the motor.
The shocks I am surprised they are as loose as you describe. The tub should move freely in the cabinet but it shouldn't bounce or oscillateit should damp out quickly.
I think mother bendix has said enough today!
Have fun with it.
jon