My idea for disposing of nuclear waste:

1. Get it into the finest powder possible, while also being soluble in water, perhaps via a combination of grinding and/or combustion and/or other chemical process.

2. Dilute in large amounts of water.

3. Release deep under the sea in the middle of the ocean

Now, most people will balk at step 3. But here is why I think it is actually safe:

a. Each nucleotide only emits radiation a small integer number of times as it falls though some decay chain. After which it is no longer a radioactive nucleotide.

b. One radionuclide is not dangerous. The average human experiences 4,430 decays per second just from the potassium in their body.

c. The radionuclides will diffuse and spread out widely across the ocean, hyper-diluting the radioactivity

d. Hyperdilute radioactivity is already with us and quite normal (see point b about potassium).

e. If the release point in the ocean is remote enough and fenced such that people are made aware to stay 100km away from it (for example) for a while after insertion, people can avoid the concentrations of radiation that are dangerous.

f. It doesn't matter that the half-life is very long (100,000 years) if the particles are broadly spread out.

g. It might matter that some of these components are foreign to Earth (only otherwise created in supernovas and long-ago decayed on natural Earth) as they may have foreign and strange chemical properties. But probably not.