I disassembled the unit using the AppliancePartsPros videos as a guide to build my confidence that I could do so. Thank you folks for providing that service to us do-it-yourselfers!
I found the leaky drain hose which had developed a pinhole, I also had another very small leak that I could not locate, possibly around the door boot seal. Knowing I couldn't locate that leak I ordered all of the gaskets and replaced them, including the tub seal. This was very easy to do, and I'd recommend it to anyone trying to extend the life of their washer.
I had suspected a broken spider initially, due to the sounds the washer made during spin cycles, but as I disassembled the tub and drum assemblies, the spider was in great shape (10-year old unit). I decided to replace the shock absorbers and dampeners for good measure.
Wow, what a difference. It runs like it did when we bought it. No leaks, and the drum stays well balanced throughout the cycle, it doesn't vibrate anymore or knock. You can hardly tell it's running, actually.
The parts can be found cheaper elsewhere, but for the service and confidence that APP.com provides it's a small price to pay for what they've done for us and I commend that.