An instant I mean as a "line of simultaneity", the events which share the same value of t in the frame to which it pertains.
So I am thinking of the rocket's frame, in which the rocket is not moving, and an observer's frame, in which the rocket is
moving. An instant in the observer's frame is the set of events which share the same value of t. This "observer's instant" is not an instant in the rocket's frame, but a set of events which we can work out using lorentz transformations.
An instant in the rocket's frame, in which clocks at the nose and the tail read the same, is similarly not an instant in the observer's frame.
If we pick any instant in the observer's
frame, and look at the rocket, we will see that clock on the nose reads less than the clock on the tail. We agree about this.
What I am saying is that the nose reaches any given observer's instant before the tail.
Imagine that we sit in two separate time machines, machines that shunt us into the future at faster rate than normal life (like fun events seem to do). We each have a watch, and we synchronise them before we switch our machines on.
If my machine shunts me into the future twice as quickly than yours, which one of us will have more time on their watch? I put it to you that the one who reaches the future first will have less time on their watch (that means me).
I agree that if we were worried about who is able to say 5 minutes have elapsed on their watch first, then that will be you. If we both turn off our machines when five minutes have elapsed on our watches (inside the time machines), you will have to wait around a while for me to turn my machine off, and will be able to say that your watch read 5 minutes first. But ... I will have gone further into the future than you.
Now, this was just an explanation, I am not suggesting that such time machines are possible. Just try to apply the same logic to the rocket and the two clocks. Relative to an observer not at rest relative to the rocket, the clock on the nose travels into the observer's future faster than the clock on the tail. The clock on the tail travels into the observer's future faster than the observer.
The observer also moves into the clocks' future faster than the clocks do.
This is where it gets less like semantics and more like something interesting ... can you model that? Not just wave it away, not just say "that's just relativity", not just show the mathematics on what must happen, but describe a model in which that is possible.
This also may be the point at which I get stomped on, so if you feel like coming back with "can you?" then I will have to politely decline.