The tile went up without incident. I decided to stop it just under the shelf. It would be a huge problem (and lots of weird cuts) to run it all the way up to the ceiling and through the structural cables. The top row ended at a very good place for the shelf, where the range hood chimney cover could end without any cutting or special fabrication.
The shelf was something else. I knew it would be tough because it needed to fit exactly between the two vertical slabs that are not very square to the wall. I also needed to provide support through the length. I did not want the supports to show, so I set steel pins into the studs and had to drill corresponding holes in the edge of the shelf. Good luck with that, right?
I measured very carefully and did my best to drill level. I still needed to drill the shelf holes oversize to get the pins to go in. I do not have photos of me pounding on the shelf with a sledge hammer to get it to the wall. But it did get there.
This part of the kitchen is basically done. Now on to the island.