From your question, you seek a technology to keep crew members alive for 200 years in an unconscious state. But you also want a plausible explanation of how this technology works. You’ve presented two possible technological approaches - cryo-stasis (presumably some kind of freezing, or perhaps artificially induced hibernation) and a motion-induced local time field within the ship (one for each crew member).
For me, the freezing/hibernation angle seems much more plausible then the one you’re leaning toward. Yes, simply freezing a person solid would kill the crew member. Water within her cells would freeze, expand and rupture cell walls, capillaries, etc. But a compound technological approach of cooling and hibernation could work well.
I read a long time ago about research into people who had drowned in cold water and been revived hours later without brain damage. How? The cold had slowed their metabolism. Cold blooded animals for example, need far less food, water and oxygen to live than warm blooded ones do. Certain chemicals it was mentioned could trigger the effect as well, causing cells in mammals to shift into a cold-blooded mode of operation. Sorry, I wish I could remember more of the specifics.
Various other forms of biological manipulation of a hibernating crew member’s biology could also be employed with technology drawn from the natural world.
An adult immortal jellyfish (Turritopsis dohrinii) when injured can revert to it’s juvenile state and eventually become a healthy adult again. Barring predation and disease, this can theoretically go on indefinitely making it biologically immortal. Eventually, how this works will be learned. In your future universe, this could form the basis of some kind of cell therapy continually applied to hibernating crew members.
Several species of aquatic animals that live in arctic waters have a natural antifreeze in their blood. This could be applied to cryostasis to prevent cell damage from freezing.
And of course, modern medical techniques can keep comatose patients alive for years with assisted breathing, intravenous food, etc.
In comparison, spinning crew members at billions of rpm’s seems fraught. As with freezing, the centrifugal forces would be most dangerous at the cellular, and even molecular level. And worst, they would not be evenly applied. Those cells farthest from the center of axis would receive far greater forces then those at the center. I can’t imagine this failing to liquifying the crew member tearing apart tissue, proteins, even their DNA.
Further, the interior time field would need to be more than slower, it would need to be zero. Otherwise, how would you feed and oxygenate the crew member? A chamber spinning that fast would need to hang in a magnetic field or something. Otherwise the friction at any mechanical connection point between the chamber and the ship would melt. If the interior time field weren’t zero, you’d have to put the crew member to sleep which brings us back to hibernation.
And consider the impact to the ship. Multiple chambers spinning at light speed would increase in mass exponentially. The energy to drive them would be enormous, and they would likely function as ultra-powerful gyroscopes working against the stability of the ship. And what kind of miracle computer could time the firing of the magnets that spun them? Couldn’t such a computer just perform whatever functions the crew would provide? Each solution needs some other miracle technology to solve the problems it generates. So you’re just kicking the can down the road.
So while the spinning chambers might seem more original, between the two, I would go with the hibernation angle. The trick to making if fresh for audiences (this scifi technology has been done to death after all) is to research the particulars and apply them to the narrative.
What I think seems fake about hibernation in science fiction is not the technology, it’s the speed of recovery. Crew members frozen solid or comatose for years just wake up and bound out of bed, ready for action. In contrast, imagine a grueling 3 month recovery process where 1 in 10 crew-members suffered some permanent damage or even died. All serious medical procedures have complications after all.
There is of course a third option.
In scifi narrative, fictional technologies present in three forms: mysterious, convincing, and yes, unconvincing. The safest route for writers introducing technology is to leave it unexplained, a mystery, which they do all the time.
From HG Wells’ time machine, the battery packs of Star Trek phasers, or the monoliths of 2001, writers routinely construct effective stories without explaining their sometimes miraculous technologies at all. How exactly do the alien monoliths of 2001 change the minds of apes to alter the evolution of humanity? Who knows? They just do.
Hope this helps.