Personally, I think you make it as dangerous as possible. So rather than shielding the waste, make it deadly in a matter of hours or minutes.

This won't prevent people from trying to extract the contents, but it should prevent them for succeeding. I think a few dead grave robbers / explorers is preferable to the waste being extracted and sold back to civilization.

It has to go from safe to deadly very quickly so that people can more easily connect the dots too.

People were trying to find a way through the artic from the 16th century, 400 years before the first Geiger–Müller tube was made.

I was thinking more along the lines of burying it deep under an inactive seabed. We’d have a hard time now digging things up. We aren’t even able to do simple floor mining well.

I imagine the sea is extremely hard to work in and salt water is very corrosive.