Thanks Freddie, currently those are correct measurements. I'll add a piece of 1/2" plywood on the top of the tread, then padded carpet.. I should get to the mandated 4" opening or just close enough. I'm pretty sure my Building inspector is just going to look at them and say they are OK,, he's pretty cool. If I have to, I may screw on sheets of clear lucite on the back of each tread to cover the opening, then remove them once the inspector is gone. I certainly won't leave lucite on the backs of the treads for very long.. I need to check out the price of lucite.
I cut some slate yesterday afternoon, and started to lay out a pattern for the floor.. It will look very nice if it works out right..
So far, the issues are the transition around the base of the stairs, where the wood floor in the family room will end and the tile and the base of the stairs start. This so far is an awkward corner.. I need to do more experimenting.
And, the centering of the tile in the foyer determines the centering of the tile in the 'U' shaped kitchen floor.. so this needs to be laid out and a bit of head-scratching done.. so far the measurements say it will work out.
Here are some preliminary photos of the layout. I will narrow the border pieces by 1" so that the large pieces will fit without trimming the corners. Or, I may have to adjust the border by an inch or so to get the pieces to center up on the kitchen correctly. Don't know yet.. I have a lot more trial and error mockups to go.

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BUT, the look I want is there, I like what I laid out on the floor, it looks very close to what I had in my mind..