I am going to have to take this a little at a time, especially since you seem to be adding unnecessary elements. But we'll see..
So it is the station's frame
Okay, being the station's frame, we know that Einstein traveled 7 from x0
during his .5c run because we know that the stationmaster saw the clocks reading 10, thus they had to actually be at 14, when he pressed the button. And we know that the train (Einstein) was at 6 from the first clock at 4 from the button when the button was pressed. The train then was at 10 from the button when it was pressed.
So, I have to assume that you have x=0 at t=0 (which wasn't intended, but I think is okay).
xE (x location of Einstein) = 0
xE = 7
So at that point, the button gets pressed (t=14), thus
Button Press == (14,7)S
Adding 6 to the (14,7)s = (14,13
)s as the state for the clock when the button is pressed.
(14,13)s + 4 = (14,17)s = button state.
(14,13)s + 8 = (14,21) = second clock state.
I think it will do.
The orange parts, I don't believe are relevant, but otherwise okay.
Where Einstein was when he saw the flashed stop-time is irrelevant. If he was 20 meters back, he would merely see the same image a little later.
I will get to the rest shortly..