In that time frame, it does not matter how many people are sent - the systems will fail long before the journey ends, triple or quadruple redundant backups will fail, every thing will fall apart. 6300 years is longer than the current civilization has lasted.
I’d think the first generation born en route (and that just a few years into the flight) would be VERY pissed they were stuck on a spaceship for life, never to set foot on Earth or any other planet. It would get ugly real fast, and they’d probably mutiny to turn the ship around and get home within their lifetime.
The only viable alternative would be a “sleeper ship” or finding a way to drastically improve speed (or both). 100 years is one thing, but thousands ? Forget it.