Yes, lots of my engines are on Youtube.
Okay, so I tried an experiment today. First, I did the color buffing of the engine parts shown in the OP. What that is, is simply a finer abrasive buffing compound called "rouge" is used to supposedly bring out the natural color of the metal, so it is called "color buffing". Whatever it is, it definitely is noticeable and much more shiny and jewelery like in its finish.
Then I got two stainless steel spaghetti pots, and in one I placed the engine parts and covered them with distilled water. I added an ounce or so of liquid dish soap and brought it to a boil. The other pot I also filled up to the same level with distilled water and brought it to a boil. This was for the rinse water.
At first, nothing much seemed to be happening. Then I used the mixer to stir the water, and it did start to get a little dirty. But mostly it made suds that obscured what I wanted to look at.
Then I remembered I have an electric back massager so I got it and used it to vibrate the pot. I could see the 'waves' vibrating in the water, and it definitely started to get dirtier.
I pulled the parts out, dipped them in the boiling rinse water and set them on a towel. The good news is that the shiny finish was not degraded one bit. And for the most part, the buffing compound residue was washed away. Some remains, but I believe if I had left the parts in the soapy solution longer it probably would all be gone from them. I only left them in for about 5 minutes and vibrated it for about 2 minutes.
Anyway, I think this is going to be a viable method for getting rid of the gunk. Thanks to everyone here for posting your tips and ideas!
BTW, I checked my little US cleaner and about the only thing that will fit in there are the valve covers.
PS: It's very difficult to get a clear photo of the polished center section because the shine reflects the camera flash.