OT: The thing about a wormhole while still opening its own can of worms does solve the issue of dealing with static build up since using a wormhole will make the trip fairly short. It also deals the issue of logistics since it would require a bit less (but still a lot) resources needed to sustain such a project.
Manipulating a blackhole would be a mamoth task, massive. I doubt the Milkyways civilisations could accomplish it even if they had a million years to do that.
Also, the talk about wormholes and Blackholes doesn't really make sense.
On the other hand, the mass effect lore stated that you could by pass such obstacles while using a relay, the Omega relay that lead to the collectorbase at the centre of the galaxy... Apparently nothign itneracts with you durign transit from one relay to the other... Though, there is no relay on the receiving side in Andromeda.
Lore also states that a ship triggering their normal mass effect FTL inside a system has a high risk of hitting a solid object... So that doesn't seem to work since Black holes are solid inside and with a massive gravitywell. Wasn't there even lore saying that you needed to get a certain distance from a gravity well to initiate FTL?
Black holes don't seem to be ideal for any kind or travel known by the Mass Effect species.
They could throw in a massive amount of Handwavium of some new type and pretend that's that. But why bother, when you can put people in cryo and let it take as much time as it takes.
All energy radiates given enough time. Just let the colonists travel in cryo like Javik and let an Autopilot do the piloting, possibly waking people when necessary. It's irelevant if it takes 1 min, 200 years, or 50 000 years. When they get to Andromeda they are cut off unless they link the two Galaxies with a new type of superior relays.