But our traveller is NOT travelling faster than light. He is travelling at 99% luminal velocity and therefore NOT travelling backwards in time. The transmission is NOT travelling anywhere either. It is not even a transmission in the formal sense of the word. It is an extrapolation of a series of actions upon the entangled particles at the other end via the observation of changes to the entangled particles on your end. The entangled particles have no known physical connection to one another.
Their perceived interaction would presumably exhibit the effects of time dilation to our communicating observers, but that would be all. Wherewhenever the opposite end may be along the inertial frame, at any given point in one frame of reference it would not be at a preceding given point in that frame of reference. Maybe the resulting communications would be distorted in some weird time-dilated fashion, but that should be about it. At least, that's how understand the conjectural phenomenon. Maybe I'm wrong. Who knows?!
Stop right there. You can never observe changes in the entangled particles. You can only observe their state once, after which the entanglement is destroyed. The best you can do is observe (after the fact) that there was a correlation.
to the entangled particles on your end. The entangled particles have no known physical connection to one another.
All of that is otherwise correct, and that is why quantum entanglement cannot be called a signal. It cannot be used to transmit information, and cannot violate causality. I already said all that.
Do you understand the crucial difference between that and the Bob/Alice problem you just quoted?