It's obviously a one way trip, no one would expect to return home (at least, not to the same home that they left, in 2000 years, human civilization may not even exist when they return, they could return to a planet colonized by Apes... hey, they would make a great movie!).
But one-way trips have been proposed for planetary colonization as well, and there are a lot of people that would be willing to make that trip.
Time traveling and seeing what Earth looks like 1000 years from now by spending 30 years in a metal can (and expending an astronomical amount of energy) is a trade I would consider.
It seems to me the most likely scenario is that we perfect the ability to copy minds into an electronic computer system. Such a digital mind would no longer need most of the resources a human body would and could potentially last nigh-indefinitely. It would also be able to take advantage of both >1G (no flabby meat body) and <1G (no aging) constant accelerations. Further, a colonization effort by digital beings would only require raw resources to build more electronics and starlight for power, which expands the number of habitable places from "planets with human survivable conditions" to "basically anywhere near a star".
It seems trivializing and like an existential crisis to have all of a humans being encoded in a computer. Once you have that, why even keep it running for all time as it is? Its just a version of software you could make changes to. We are probably not as glorious as we could be to become immortal as we are.
I am not convinced there is any solution to aging. When I was a child, I read headlines that claimed a solution was close at hand. We seem only marginally closer to eliminating aging.
Importantly, how many memories do you think can fit into a human brain? If a 1,000 year old man cannot remember all of his life, has aging been solved?
Does one need to remember all of their life to be happy?
Maybe the details just get spottier with bigger gaps, but you still remember the big events and when you need more details your Google neural implant tells you more. I'm far from 1,000 but I can't remember every detail of my life, but I don't think it interferes with my quality of life.
Apart from the fact that everyone you know is now dead and if you returned home you'd basically be a living caveman museum piece.