How superluminal motion can lead to backward time travel

It is commonly asserted that superluminal particle motion can enable backward time travel, but little has been written providing details. It is shown here that the simplest example of a "closed loop" event -- a twin paradox scenario where a single spaceship both traveling out and returning back superluminally -- does {\it not} result in that ship straightforwardly returning to its starting point before it left. However, a more complicated scenario -- one where the superluminal ship first arrives at an intermediate destination moving subluminally -- can result in backwards time travel. This intermediate step might seem physically inconsequential but is shown to break Lorentz-invariance and be oddly tied to the sudden creation of a pair of spacecraft, one of which remains and one of which annihilates with the original spacecraft.