Your question posits the possibility of faster-than-light communication. That typically means a question is not concerning with mainstream physics. I say "typically" here, because there is a small but significant literature looking at possible local violations of special relativity. This is useful, for example, for understanding and quantifying the results of the current generation of updated Michelson-Morley experiments. In fact, it is something I work on myself. However, it is a fairly technical field, and mainstream work in this area has to be very careful about mathematical definitions and methods; sloppy treatments tend to descend into self-contradiction pretty quickly. So it is possible to ask questions about, say, how well the possibility of faster-than-light signaling in various experiments has been experimentally constrained, but useful questions of that nature generally require a much more sophisticate treatment that the one in your question.
Moreover, the question specifically talks about signaling that is superluminal but not instantaneous. However, that turns out to be an illusory distinction in relativity. The very first thing that Einstein showed in his first 1905 special relativity paper was that the invariance of the speed of light (that, as observed in the Michelson-Morley experiment, the speed of light is observed to be the same by all observers, regardless of their own velocities) meant that different observers would not generally agree on whether two events were simultaneous. What this means for faster-than-light travel or communication is that while one observer may see signals being sent faster than light, others will see signals being sent instantaneously (that is, with infinite apparent speed), and still others will see them going backwards in time. So it is difficult to see how your proposal for faster-than-light but not instantaneous communication could be at all consistent with what we understand about relativistic physics.
