"might as well just send it into the sun."

The Sun requires more delta-v to hit than compared to the Moon- it's even lower than High Earth orbit

"Don't forget to factor in the density of uranium in your calculations."

Radioactive Uranium isn't isn't waste, it's fuel.
But yeah, I was going to mention that, you probably start off shipping radiactive waste which had lower density, and you might focus on any type of waste which was more difficult to store long term.
And all of this depends on cost- if it's cheaper to store on Earth somewhere, you store it there instead shipping to the Moon. But I believe the current price to store radioactive material is quite high- 100's dollars per lb. If the price of storing radioactive material were to go lower to somewhere around $10 per lb [which is quite possible], then chemical rockets probably wouldn't be competitive- you would need things like space elevators or something more realistic like an Orion:)