... Time travel is allowed for by GR, and many reputable physicists and opinions are open on that score: Difficult? Beyond our means at present? Yes certainly, but not impossible according to our knowledge at this time.
I don't think you can show time travel is allowed by GR (or any other scientific argument) because neither the future, nor the past, even exist now.
Going to Peter Pan's Never Never Land, NNL, is also not forbidden by GR. That, like time travel, is impossible because it these destinations (NNL, Future & Past) do not now exist. Only the evolving "now" exists.
More advanced technology, will not change this fact.
You can not call a slowed rate of aging "time travel." The are several existing ways to live longer and let what is now a non-existing future become your "now." Exercise, regular medical check ups, proper diet will all on average do that, but they are not "time travel." Suspended animation and spending 30 of your years in a fast moving space ship, neither of which is impossible now, would not be time travel either - just slowed rate of aging compared to time lapse on earth's calendars.
Many are using medial check ups, proper diet, and exercise to live longer. I. e. experience the world that will come into existence from the more distant future than if they did not do these common means of slowing their rate of aging.
but they are not time travelers.
Some day, a fat lazy slob, who will not do theses things, may be able to celebrate his birthday and New Year's eve of the year 200 years after he was born, via suspended animation.
This not time travel.
Some day a rich, but fatally sick man, may make a fast round trip thru space, and return 100 earth calendar years later, when medical science has found a cure for his fatal disease.
This is not time travel.
All these methods, some now even possible, are not time travel - they are slower rates of aging in comparison to people remaining on earth so your death date is after more earth calendar years have passed. Some day, if rich enough and technology has advanced, you might be able to experience the first 365 days of each new century on earth, before getting back into your space ship.
This, getting to experience the changes each 100 years brings, is an interesting idea, not prohibited by GR, but also
is not time travel
SUMMARY:
Time travel is impossible as the future (or past) you would travel to, like Never Never Land DOES NOT EXIST. This is not a technological limitation to over come; but yes, GR does permit you to live only one year on Earth at the start of each earth century for three or four millenniums. (Assuming that when you return to earth, in say earth calender year 2700, the population then on earth does not sterilize your space ship and all that is in it as a protection against ancient medical diseases, like the common cold, etc.)
You confuse slower rate of aging, which is possible, with time travel, which is not possible.
PS:
To believe true time travel is possible, you must believe some where NOW a future we will evolve to already exists for you to travel to. I. e. that you could visit them and try out their tele-porter machine that exist on each street corner, as cars were abandoned 100s of years earlier. etc. That also requires you to believe you have a pre-determined future. No choices.