What "science" do you use to design mechanisms to keep highly toxic materials away from human contact for 200,000 years?
It is not science. There is no science that can solve those problems. It is greed.
(I live in the South Pacific. The French are hated here for what they have done for their nuclear programme)
Alternative first step: build breeder reactors to recycle most of the waste into nuclear fuel and dump the smaller amount of leftovers in the mountain.
Where?
Where on Earth will you find a place that will still be like that in 200,000 years.
After a few hundred years it's no more radioactive than the rocks from which it came.
You seem to have the common misconception that "long half-life" = "more radioactive", when in fact "long half-life" = "less radioactive", by definition.
The other main thing to remember when burying nuclear waste is that it's important to keep it away from aquifers and generally any flow of water under the ground. Obviously you'd probably want to seal it in waterproof containers anyway, but it's better to not have to rely on the container staying intact over long spans of time.