That would imply that the train is not length contracted in $$S''$$.
No, it doesn't , it simply means exactly what I said, that you are unable to measure $$t"=-\frac{Vk\gamma'}{c^2}$$. I challenged you to do that and you are still fumbling and bumbling but you have no ability to answer.
Please demonstrate length contraction in $$S''$$ without using $$t''$$.
Nice try, I can demonstrate length contraction using the plane of simultaneity in $$S"$$ , $$dt"=0$$ (as I have already done) , this doesn't mean that the timestamps can be measured, as you amply demonstrate in you inability to do so.