You need ten times the mass of Mt. Everest in e=mc^2 energy (i.e. 100% efficiency) per 1 kg of mass to get to Andromeda at 1g acceleration/deceleration. [0]
For this reason I sincerely hope that conservation of mass/energy is not necessarily true. Nothing says it needs to be true other than that it empirically seems to be the case, and there is no known process that violates it, other than the Big Bang itself. If it can be violated, we have hope for the long long long term future.
Scary to think about this stuff.
[0] https://en.wikipedia.org/wiki/Intergalactic_travel
[1] https://en.wikipedia.org/wiki/Timeline_of_the_far_future