David Brin had the solution
tectonic subduction zones.
Instead of finding the most geologically stable areas for your dump - sorry, storage facility - dump the waste into an area where crustal plates are being driven under.
Encase the waste so it will be protected for a couple of centuries, and let natural processes bury and dispose of it. Monitor the area for security purposes, to avoid the "eco-terrorist stealing some to use a weapon" cliche.
The Earth is naturally radioactive, even enriched waste wont make any difference.
Launching stuff into the sun is just too expensive and bad for the atmosphere unless we had something like a beanstalk/orbital elevator.