So, in the last project video, you could definitely hear the keys clicking when I played it.
When I looked at other keybeds, I noticed that they used stick-on felt on some surfaces to reduce that sound. I searched around and found sheets of the stuff at JoAnn Fabrics for about $2.50. I'm sure one can do better on price, but it isn't worth the time to find out for the prototype.

I cut the felt on my paper cutter for nice straight, clean edges.

Before I took the whole bloody thing apart again, I checked the length against the keyboard.

I put felt on the bottom of the spacer / keystop lips so that the hooks on the bottom of the keys would not make a noise as they rose.

And then another strip under the slot where the hooks go, so that they wouldn't make a sound if the hooks actually contacted the bottom wood.

Finally, I put a felt piece under the keys themselves, which is probably the loudest actual point of contact.

I'd love to have a video of how quiet it now is here for you, but I found some other problems (middle "C" not working) so the whole thing has been disassembled on my desk again. But, for a brief, shining moment, it was quiet!

Edit: Ok, I fixed it! All of the keys now work. Still some key noise on key up... evidently the felt I put there wasn't enough?
Meh. Here is a video.