Instead as you said we could yeet it all into space with like 20 starship launches, taking the $100/kg price tag it would cost us 2 million dollars to send it to space. Starship electronics should be radiation hardened so the unique payload shouldn't affect it much. The only risk is starship blowing up during launch. That would be a bummer.
There's already a paper discussing this[3].
I love the last line in the paper
'Both the technology and the need exist. What does not yet exist is the will and support of the engineering and political communities'
Mind you this came out in 1992, we have far better technology now.
[1]https://www.scientificamerican.com/article/nuclear-waste-let.... [2]https://earth.stanford.edu/news/steep-costs-nuclear-waste-us... [3]https://space.nss.org/wp-content/uploads/Space-Manufacturing...