"I guess I hadn't thought of that. If you could get it as far as the moon couldn't you sling shot it out of the earth-moon system getting a gravity assist from the moon?"

Yeah, and probably using gravity assists from Venus or Mercury, you could get your nuclear payload close enough to the Sun to incinerate it.
But if you can get to the Moon to do the gravity assist, you can just as easily impact the Moon- with an impact speed of say 2.5 km sec. With an impact speed of 2.5 or less you shouldn't have much of a problem with the payload vaporizing and spreading around the Moon. Add to this a smart containment system and you could probably keep the nuclear material within a mile of it's impact. Which means that if you had a 50 mile diameter crater you could put all of the nuclear waste from Earth in that crater and it wouldn't be dangerous and could be future resource.
Another idea could be to put waste in Earth/Moon L4/5 or Sun/Earth L4/5. The L4/5 unlike the other L-points is graviationally stable for millions (or billions) of years. Probably the safest would be Sun/Earth L4/5, simply cause it's far from Earth, and chances of any impacting Earth over millions of years (without any human intervention) would be lowest. Either of the L4/5 would as easy as putting a payload in a 50 mile diameter crater on the Moon and probably easier to use in the future.