Intergalactic voyages are long, they go over quite large distances, but you, a human in the Milky Way, want to see a galaxy beyond our own with your own eyes and live there. At 99% the speed of light, the journey to Centaurus A, your destination, will take you 14 million years in real time, but due to special relativity it will appear to be 2 million years. That sure is an improvement, but despite the advances in life-extension technology, no human or alien has survived more than 10,000 years of relative time.
Also, like most people, you are afraid that if you freeze your body, when you wake up again, you will be dead, so joining a sleeper crew is not an option for you. How much do you need to abuse general and special relativity in order to get the travel time down to around 9,000 years, short enough you can spend your latter days in the galaxy of your choice. How much faster will you need to go, or how much bigger of a black hole will you need to have, in order to survive a trip to more and more distant galaxies?
For the sake of the question, just assume that we have powerful enough protection that being hit by particles in the intergalactic void or CMB radiation isn't an issue and that we can move a black hole of arbitrary size at any relativistic speed without breaking anything. Feel free to talk about how unrealistic the contraption is you come up with, but right now I am trying to understand how much general relativity and special relativity impact the subjective experience of time.
Also, the ship can't be in the black hole event horizon obviously so there's probably no need to have a black hole of any size as there is probably a maximum amount of time dialation you can get from general relativity while remaining outside of the event horizon.