Here are 2 ships passing in opposite directions.

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?

I think that the term "same moment" is self-explanatory.
Go ahead and try to draw some diagrams showing before the moment of T of ship1 lining up with N of ship2, the moment of T of ship1 lining up with N of ship2, and after the moment of T of ship1 lining up with N of ship2 from the viewpoint of each ship being at rest. Be sure to show both ships in the diagrams and the 4 clocks in total which are placed at the T and the N of both ships in all of the diagrams. If you do that you will see that there is a problem; T of ship1 passes N of ship2 twice.

And that is your problem. By "self-explanatory" you mean that it is something that seems right even though you haven't tested it.

In this case you are wrong. And, that is why you are getting the wrong answer.

I am serious.

There are very good courses on special relativity available for free online. Why don't you take one?

Why don't you do what I ask and see for yourself that special relativity is invalid?

Your entire chain of reasoning is based on a flawed assumption. You are assuming that there is a "same moment" that is shared in multiple reference frames. In reality, there isn't. If you fix your mistake, your problem goes away.

This is a standard exercise in special relativity that is solved (without problem) by every college student and high school student who studies this topic.

Ship1 at rest at top.

Ship2 at rest at bottom.

T of ship1 passes N of ship2 twice.
Once at 9:55 for N of ship1 and again at 10:00 for N of ship1.
Once at 10:00 for T of ship2 and again at 10:05 for T of ship2.
Maybe you can explain this.

Define 9:55?

Are you saying that on the first ship, someone set their digital watch at some point and now it is reading 9:55? You are stating by edict that some absolute time exists. In reality there is no absolute time. That is your mistake.

You are making a circular argument... "since I know that absolute time exists therefore absolute time exists". If you drop the idea that there is absolute time, your mathematical problems go away.

Let's talk about how science works.

Special relativity posits that there is no "absolute time". By this I mean that the time elapsed in one frame of reference will be different than one observed in a different frame of reference.

The claim make by special relativity is that there is no universal time keeper. That the elapsed time as measured in different reference frames are equally valid. One person can't say that their frame of reference is the official one.

There is a system of mathematics that maps measurements in one frame of reference to the measurements in another. This is the Lorentz transformations that you have obviously see. After a little study, anyone can learn to do these transformations.

But having a mathematical system doesn't make it correct. What makes it correct is experiments We take the predictions made by this mathematical system and compare it to reality. It turns out that this particular mathematical system works to explain reality better than any other model. That is why we accept it.

The more fun, and counter-intuitive version of this problem is the very fast train in tunnel problem.

1) Alice is standing motionless relative to tunnel and sees the train as shorter than the tunnel. Alice has a button that closes gates at the entrance and exit of the tunnel for an instant when the train is inside the tunnel.

2) Bob is standing motionless relative to the train (being inside the train). He sees the the tunnel as shorter than the train.

What is counter-intuitive is how a larger train can fit inside a smaller tunnel when the doors are closed. Of course, if the train crashes into the closed gate in Alices frame of reference, it must also crash into the gate in Bob's.

Of course, the mathematics has a cool answer for this problem. To Alice the gates are closing and reopening at the same time. To Bob, the exit door and entrance door don't close at the same time (the exit door closes and then reopens first before the front of the train arrives there, and the entrance door closes after the end of the train passes). The train doesn't crash in either frame of reference.

The mathematics is cool and it works (if you do it correctly). What makes the mathematics correct is that it is the only model that explains what we see in reality through experiment. The fact that it is kind of cool and counter-intuitive is just a bonus.