Because that star system would have to consist of a massive Black Hole, and to "loop around," as you say, you would have to practically "skim" the Black Hole's Event Horizon.
By the time you reached max. velocity, at the Galaxy's edge, and wanted to reverse your direction and go home, you would have a velocity of, say, 0.99997 c ("c" = velocity of light). Doing a "flyby" (as is routinely done by Nasa's space probes, when they swing by Jupiter or Saturn or such to get an extra little "push" and speed them on their way to, say, Neptune) can never increase / decrease your velocity by more than the escape velocity of the celestial body you are swinging by.
Thus, only Black Holes would be suitable for your purpose.
Since you would be in free fall, you would not feel the sudden deceleration and acceleration as you rounded the Black Hole - but the tidal forces (see Larry Niven's "Neutron Star") would make spaghetti of you.
Regards,
Skimming the gravitational pull outer limits (is that same as the Hill Sphere of a star?) black holes sounds like a risky endeavor akin to snake charming or placing head in lions mouth at the circus
And the mass density issues I assume start there no?
One analogous description of black hole density always stuck with me....a thimble of Black Hole matter in a black hole would have the weight of a full supertanker
That’s exponentially more than pressures at our deepest ocean depths
14.5 more pounds pressure every 33 feet of depth
I guess challenger deep pressure is 15,000 psi
But in reality I’m wrong I think because isn’t the point of massive density in a black hole the absolute center?
Some scientists say an all consuming black hole can be less dense than water except that precise center of the hole
It’s over my head