Yes it's 300 years, because of magic which somehow makes recycling feasible and let's us ignore all the parts which have lifetimes longer than 300 years. That's not a valid argument. So far nobody has managed to come up with a economically and ecologically feasible way to recycle nuclear waste. The French Le Havre site is primarily run for military reasons and multiples the amount of waste. Admittedly lower grade waste, but it still needs to be kept away from people for thousands of years.

Even if it was a million years it wouldn't matter. The US has the Nevada desert which is effectively a barren wasteland, just shove it in a bunch of containers and leave it there. They already do that for removed nuclear reactors from military vessels (which is actually so it can be seen in satellite imagery to fulfill international treaty requirements.