Heh, many years ago I actually designed the theory for a FTL communication channel - all I needed was a way to use N remotely entangled particles to generate N+1 of them (or a serious boatload of particles to start with). The essential element being that, while random, the probability distribution can in fact be manipulated. It makes for a very "noisy" transmission medium, but with enough redundant bandwidth it should be possible to get a message through.
Essentially your design boils down to "I have a process which transmits zero information. If I multiply the process x times I will transmit a positive amount of information".
The sender is doing ZERO information transmittal. None. And no amount of handwaving will change that. This is the equivalent of perpetual motion machine designers arguing that they added the right combination of cogs and parts to violate the laws of thermodynamics. If you understand the underlying principle, you no longer need to try to understand how the perpetual motion machine is design to know that it impossible.