There is no v in the problem you're setting up. The whole point of relativity is that S2 is not receding. No observer attached to the ship can measure any such v. There is no dragging of the speed of light. The measured speed for light inside the ship is c, not c-v, as you claim. You got everything wrong. This v is only in your mind. So the very first time you wrote an equation and you said you were going to hold it against relativity. Well... You wrote the wrong equation. S2 is not receding from the POV of anybody anchored to the ship --at rest relative to it.
Nobody, repeat, nobody stuck to the ship has any right to even start talking about such v. What v? What are you talking about?
What you are doing is using a quantity that only makes sense in the frame attached to a certain "rest observer" you're telling us nothing about in your calculations about another frame.
And yes, according to your main line of reasoning, space within a ship is non-isotropic, which is a ludicrous claim, of course.
(My emphasis.)
What?! This is false. In the ship's inertial system such time is t=D/c, not what you say.
The whole thing is ridiculous.