GE WWSE5200B1WW Clothes Washer Agitator Main Shaft wiggles a lot

My GE Agitator Clothes Washer has worked fine for years, but this week it began leaking a small amount of water, and the Agitator does not Agitate.

The leaking does not begin until the Tub is entirely full. I removed the Front Panel, but cannot find the source of the leak. It is definitely not the Pump, Pump Hoses, or Water Hose Inlets, as I inspected and felt them - all are very dry. I can't find any dripping, which leads me to believe it must be towards the rear right corner.

The entire Floor Pan is oily and greasy. Perhaps the Transmission has leaked out all it's internal oil ?

The Agitator does not even move at first, but begins slowly to spin faster and faster. The WASH CYCLE will complete, spins and pumps.

After a Wash Cycle, before I removed any clothes, I tried a SPIN CYCLE alone, and it spins just fine, and the clothes inside are simply damp; as they should be.

I have noticed the Agitator has been loose and rocked a lot for months, but as all was well otherwise, I figured this was normal.

Right now I have the Front Panel off, the Agitator out (it came out very easily), and am waiting for the proper WRENCH to arrive.

I've ordered a new TUB SEAL, NUT, SPLIT-RING, TUB BEARING, with the washers that go with them.

I hope these will solve my problems, but fear the TRANSMISSION may be gone. In that case all will be scrap. I'm not putting $200 into a 7-year-old machine.

Advice ? Please ?