Instead of starting the engine to slow down at the edge of the galaxy and then build speed back up, why not do a loop around a star system to maintain your current velocity so as to be more fuel efficient not to mention saving time on the return trip.
100,000 years might be enough time for the apes to build a civilization so you can return and do your best Charlton Heston impression upon seeing the Statue of Liberty.
I went back to a thread that does the math, and a slight correction (hey, I read this awhile ago). 20 years to get to the center of the galaxy, and 20 years to get back - 40 years, doable in one lifetime. For Alpha Centauri, it is 7 years to go and return.
The numbers to the center of the galaxy:
Ship time: 19.8 years
Earth time: 27,002 years
Peak velocity about 77 cm/sec less than c.
To Alpha centauri:
Ship time: 3.6 years
Earth time: 5.9 years
Peak velocity: 95% c
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,
The turning radius of a Tesla Roadster at lightspeed isn’t all that great.