But we're puny.
And we'll never succeed to cross the vast interstellar distances like this, it'll just all take too long to 'get up to speed', cruise through space for millennia, then 'decelerate at the other end'.
"There's always a bigger fish," Jedi Master, Qui-Gon Jinn.
We should lsten to this 'jedi master' and LOOK FOR THAT BIGGER FISH, out there in the universe. It's time we invest some observational tech on looking for the BIG STUFF, the universal carrier pigeons that are already spanning the universe, already leaping from galaxy to galaxy. We need to raise our mathematical-navel-gaze up from the Planck Length where Science thinks answers may lie and concentrate on the more-holistic MACROSCOPIC UNIVERSE so that we can take advantage of the natural phenomena that are already active in intergalactic travel.
In the same way that a tick hitches a ride on the flank of a wildebeest, covering far more distance as a PARASITE than it ever could crawling through the enormous stalks of the grass lands.
I suspect there are VAST intergalactic entities surfing through space, large as galactic clusters, physical anomalies that allow SMALL STUFF like us to 'hitch a ride through space on the back of them'. You might want to call it 'extra dimensions' but you don't necessarily have to, it's just A VERY BIG THING that could carry something very small on its moving surface. A turtle in a gulf stream. A barnacle on a whale.
Think about the way the entire universe condenses out of its intergalactic super structure. Get something BIG (and mobile) to give you a hand across freezing cold river, you know, rather than trying to swim the chilling gulf yourself.