It's fixed!

First I verified that there were no shorts in the contacts, and I checked the continuity of the closing contacts. They all seemed OK, but I cleaned them anyway (I was surprised to find some spiderweb inside the dial pad). Still no improvement after that.

Then I compared the individual row tones against the correct frequencies from a software tone generator. It was difficult to tell, but they seemed a bit low to me. I adjusted one of the two transformers by only 1/2 turn clockwise, and bingo! All keys now work!

Big thanks to all who helped! I learned a lot in the process, it was fun, and I now have a great looking phone on my kitchen wall.

Mike