I suppose you could accelerate in an orbit around earth to maintain contact. But my understanding of relativity is poor
I think your misunderstanding comes from the relativistic twin paradox.
From the perspective of the twin on the spaceship accelerating away from earth, the twin on earth seems to age slowly as well until the space ship twin decelerates and then turns around, during which they perceive the twin on earth to age rapidly.
The acceleration / deceleration of the space ship twin’s frame of reference is what breaks the symmetry of the no-preferred frame of reference during flight.
I'm sure producing one of these things is more possible right now than freezing/thawing/reviving a human.
Alternatively, to compensate for how long it would take to speed up and slow down, just have our intrepid time-o-naut climb into their suspended animatio--- oh heck ;)