To figure out what was wrong and to see the parts better, I followed online video instructions to take out and disassemble the dishwasher, removing the motor and pump assembly before ordering replacements. I cleaned the old parts and reinstalled the whole thing but it still howled.
I went online and (for this Kenmore washer) found a SearsParts site, but I was not confident that the replacement indicated was the right one. (And I'm pretty sure it wasn't.)
I then went onto AppliancePartsPros.com. I found what looked like the right assembly by searching by model number, and then was delighted to see that the part was listed with ALL (a huge number) of model numbers that it fit -- including the one I had put in. Thus when ordering I was quite confident I'd get the right parts. And I did.
I used the moderate speed delivery option (3-5 days, I think) but it was shipped the same day I ordered it and showed up the next day.
I disassembled the unit again, installed the new motor and pump assembly successfully and all is well -- except I need to replace the (compression-fit) water inlet line which has a very slow drip under my sink faucet (no fault of the repair parts). I'll replace it with a flexible hose to make future removal/installations easier.
The hardest part of the installation/reinstallation was getting under the sink to the water and drain hose connections.