I think the best approach to using this mechanism in sci-fi would involve using it for braking rather than sending. The problem with sending is that you want the black hole traveling fast in the direction that you are going and this requires creating a binary black hole system somewhere in the close interstellar neighborhood of the star you want to come from (since if it's 4 light years away you need to have already solved interstellar travel in order to travel between stars with this mechanism...)
The engineering for using one of these to brake against, just requires one to make a smallish black hole that is falling into a gas giant planet and consumes a large chunk of it to form a black hole orbiting your star. Then anyone who wants to visit you can use much more of their fuel to accelerate to a much higher speed with the confidence that they can use your black hole to slow down as they are entering your system.
The engineering for using one of these to brake against, just requires one to make a smallish black hole that is falling into a gas giant planet and consumes a large chunk of it to form a black hole orbiting your star. Then anyone who wants to visit you can use much more of their fuel to accelerate to a much higher speed with the confidence that they can use your black hole to slow down as they are entering your system.