Unless we have civilizational collapse in which case a bit of nuclear waste will be the least of our problems.
It won't have to be monitored for a 1000 years. First, by that time the level of radioactivity is very low, and when it's in a deep-geological repository (like the ones we already use for vastly greater amounts of highly toxic chemicals that never decay) it is gone. We know enough about how geology works.
We also know how a BLU-122 works. Can you be sure the US wouldn't use one on its allies in yet another moment of irrational tantrum? What about Russia?
