Another effective way to deal with the low grade waste is to pulverize it and spread the dust in the wilderness. Or mix it with concrete and build a school with it.
A concrete example: In terms of radiation dose, a depleted uranium cutting board is equivalent to granite countertops.
Most low level radioactive waste is just not that dangerous. Dilution is as effective as storage.
Amusingly, every American school I've ever been inside was built of cinderblock - a type of brick made from the fairly radioactive ashes from the exhaust of coal power plants. Don't take my word for it, ask a kid to take a Geiger counter to school one day. (I wonder if that is an expellable offense in our times?)
Why not just pack the most dangerous nuclear waste onto a rocket and blast it out of the atmosphere and out of any orbit, perhaps into the sun?? The risk is something happening to the rocket on the way up. It sounds absurd but there's a lot more radioactive things in space, and costs for such a procedure seem to be lowering.
It should be noted that the force with which the contents of an exploding rocket hit the ground is not infinite, and objects have been built to withstand it. In particular, the casing of the plutonium bricks used in the radiothermal generators which powered certain space probes had this property.
You could also have a parachute at top that would open in case the engine and fuel exploded, so long as the waste casing could withstand the forces. Also, launching on a remote island could be beneficial, but it'd increase the cost. Also, there could be smaller more frequent rockets than larger ones.
A concrete example: In terms of radiation dose, a depleted uranium cutting board is equivalent to granite countertops.
Most low level radioactive waste is just not that dangerous. Dilution is as effective as storage.