Or we could change the space treaties to allow it to be sent into the sun.
Do you have any idea what kind of energy it takes to send something to the sun? Earth's orbital speed is around 70,000 mph, that's 70,000 mph you have to decelerate your payload.
Well, we don't really care at what speed it hits the sun at, nor what damage is done to the vessel carrying it. For all that matters it could be a simple slingshot manuever to set it on the right trajectory so the craft could even be re-usable - e.g re-usable stage 1 and 2 rockets to move to orbit (see SpaceX), stage 3 connects to an existing orbiter that then takes its times (6 month? year? doesn't really matter) to set the item on trajectory, and returns. Stage 3 departs from orbiter and without using any extra fuel could make it's way into the sun - really, the sun has this awesome thing called a gravity well, and all you need to do is get the stage 3 section into that gravity well and the sun will do the rest. There's numerous methods to do it, and they're all really cheap from space. (FYI - this is basically how a mass cannon works).
BTW, the orbiter doesn't have to actually enter the gravity well, just be able to set the mass on a trajectory that it could not escape the gravity well.
Speaking of the payload, nuclear waste consists of heavy atoms. Heavier than lead, or gold. Have fun getting that even into earth/sun orbit at an acceptable cost.
1 ton of material is the same regardless of whether it is gold, feathers, or nuclear waste.
But then, who said we had to do it by the ton? We could do it in 50kg blocks for all it matters - or allow the orbiter (see above) to collect several groupings of cheaper payloads to send together.
IOW, this is really a lot cheaper than you think. The biggest cost is raising it to space to start with; and that's probably cheaper than drilling into a mountain every few years to make more capacity for additional nuclear materials, and everything else that goes into it.