There is one moment when T of ship1 is lined up with N of ship2. This moment must be the same moment for both ship1 and ship2.
You are stating that this is true, but it isn't. Tell me what the word "same moment" even means (how would you measure it). Same moment seems to mean that both of them look at their watches and see that it is 01:02:22.00000. Think about that for a second knowing that time moves at different rates in different reference frames... and you should be able to see that "same moment" doesn't mean anything.
Any basic physics text will explain this for you. A problem almost exactly the same as this is worked through by high school students in an AP class. It is a little tricky because your intuition is wrong, and dropping your intuition is always difficult.
You are spending time working through the problems that you would be working through in an actual physics class
. But you stopping just before the point that you actually learn something.
Why not just take an actual physics class?