It would be good form to actually quote at least one example of what you consider incoherent.
I've done this now, but I don't think it will be effective because your example is almost literally flawed at every point and so fundamentally ill-conceived it is hard to find a starting point from which to analyze the errors. However, after giving this some thought, I decided that the closest thing to such a starting point is your claim that "This velocity is close enough to the velocity of light so that they should apparently be significantly affected by time dilation..."
You are significantly affected by time dilation when sitting in a chair in your house. Your "argument" supposes that time dilation should affect...? What? How? Time dilation affects an observer
at rest (
i.e., with no velocity let alone one near the speed of light) relative to a moving observer traveling at speeds far, far below that of light. You seem to think that because the spaceships are travelling fast, we can therefore assume time dilation matters (we can always assume this as it is always true) but nowhere do you argue
how it is supposed to affect anything and doesn't. That is, by failing to understand what time dilation is, you simply state that special relativity holds it matters in the example you use, you don't state how, and then conclude that your example shows the absence of this effect without ever expressing how it should exist (according to special relativity).
To simplify:
1) According to special relativity, there exists a phenomenon usually called time dilation.
2) You claim that this phenomenon, according to special relativity, should exist in your thought-experiment because of the velocities of the spaceships
3) You do not state how, according to special relativity, this phenomenon is supposed to exist in your thought-experiment.
4) You then go on to claim that in you have shown in your thought experiment this phenomenon doesn't, in fact, exist.
5) Since you never explain how the theory of special relativity holds that this phenomenon should appear in your thought-experiment, you've shown only that something undefined doesn't occur in your argument because you have defined it that way.
Let us examine how an actual argument might proceed to show something like that you wish to:
1) According to Theory X, given certain conditions we should find that some set of variables or quantities (measurements of time, temperature, mass, eigenstates in Hilbert space, etc.) are altered by effect E.
2) You describe a condition C in which effect E should hold.
3) You describe how Theory X holds that E should change the relevant variables or quantities in C.
4) You then show that the changes expected by E do not occur in C.
What you don't do is claim that there should be effect E in your argument's example, but fail to specify how anything should be affected by E in this example, and then claim that we don't find the results of an effect you never described to begin with.