Well, we're in off of our ledge. we've gotten much good advice here about how to proceed. Our tile contractor hired a sub who ruined the stove and floor, and screwed up the tile job. (episode 1&2) After two weeks of silence the contractor finally got back to us, as he could smell a "demand letter" coming.

He came to our home last weekend and took his lumps, he reviewed the tile job and said the unsanded grout they used should have been perfect above a cooktop(as it seals better), he offered to have it re-grouted and gave us a lifetime warranty against cracks.
As for the tile layout itself, he looked at it without us prompting him, and offered immediately to change the way the mosaic is framed, removing some cut tiles that were bugging me.
the floor damage he has offered to repair to our satisfaction, but without redoing the entire floor.
And finally, since we disagree on the stove, he is dispatching his insurance adjuster to review.
The biggest thing was after being so dismissive for two weeks, he actually showed up on time and took responsibility for his subcontractor's sh*tty work.

I have subsequently been contacted by a lawyer who specializes in construction cases, and she called my case an easy one. She advised documenting everything, especially the before and after repairs, and don't sign any kind of receipt acknowledging completion of work

My demand letter was over $10,000, but she advised that this process could take 8 weeks or more. At this point, if we extract a pound of flesh, we'd have no place to cook it.