Anything that involves FTL uses some rubber as the fact stands, no one has ever managed to travel faster than light. You seem to want to look at equations and I diagrams. I was looking for a way to have FTL travel without time travel. One way to do that is to reduce the 360 degrees of the time/space diagram to only 180 degrees and lets say that absolute velocities cannot be negative and instead range between 0 and 1/0 in absolute magnitude. Under such an assumption FTL travel is still possible if you give it an upper and lower limit. The lower limits of FTL travel is the speed of light or c; the upper limit could be 1/0 or else it could be a lower number if you want to have more than one FTL realm. The simplest is simply to assume that there is FTL and STL. There is 0 evidence for any of this anyway, I never claimed otherwise. What I'm concerned most with is what works best for a game.So, if you want to make YTU more "real" but still preserve space or star travel, you don't need time travel, or branes or really much of anything. Wormholes and warp drive, on which there is already extensive theoretical research that has been done, and you can look up, (If you can get through the math, which I can tell is a tough one.) solve the problem, while minimizing the rubber science in your campaign. Even sticking with Jump Drive, and not changing anything, is less rubber science than what you are proposing.
The term "Jump" Drive implies that the travel is instantaneous. You jump from point a to b without traveling the distance between. Another fine way to go FTL is with one-way wormholes. You can travel one direction through the wormhole but not the other. If the wormhole itself is moving FTL, then you can only travel through it in one direction. Perhaps an FTL drive can cause that to happen. Somehow the space ahead of ths ship will have to be manipulated so as to cause the creation of an FTL wormhole opening. The other end of the wormhole also goes FTL. The "duration" of the wormhole is the distance it travels in space. The amount of space the wormhole transports is an elongated spheroid and everything within that volume of space gets transported to some other location.