"I'm not so worried about low-level nuclear waste, but high-level nuclear waste is deadly for many multiples of human recorded history into the future. "
Please stop drinking the koolaid.
Contrary to popular belief, plutonium and uranium aren't particularly radioactive unless you put a lot of the pure stuff in a small enough space for the atoms to start affecting each other and give them a bit of assistance by arranging things "just right". The greater danger is chemical - they're both highly reactive and highly carcinogenic heavy metals (depleted uranium shells are decidely _non_ radioactive. They kill tank crews more by incineration than by kinetic energy, once they get through the armour and that chemical toxicity means they will leave a nasty legacy where used for decades to come)
"spent" fuel rods are blazingly radioactive thanks to high levels of calcium, cobalt and other unstable isotopes (handling one will kill you from the gamma exposure in very short order)
However: stick 'em in a safe place for 300-400 years and that gamma emission level will have dropped to a level low enough that the rods are safe to handle without requiring special kit - and once the contents are chemically processed, they can be reused as reactor fuel (enough plutonium in them to offset the near-natural uranium balance.
If you don't want to wait that long, just dump it all into a MSR and things will be "burned down" much more quickly - the big "positive" is that given the thorium cycle's calculated efficiency, you should be able to achieve 97-98% usage of the starting fuel, instead of 1%, so the amount of "hot stuff" coming out the other side is minimal _and_ shortlived. It's better to keep "hot" stuff in the reactor and extract the heat as work than it is to dump them in the bottom of a pool and let it heat the water.
MSRs are really good at producing heat and lousy at producing plutonium (it can be done, but it's a LOT harder than any uranium/water setup), plus they don't need massive cooling (they run much hotter than traditional plants, so thermodynamic efficiency is better), can't burp gasses, melt down or explode (the nuclear side is all unpressurised) - and the lack of water in the nuclear loop means they can't leak thousands of gallons of low-level contaminated water either. That makes them a far "safer" system from actual risk point of view.
The steam turbine side comes with the usual issues of steam plants, but that can be entirely decoupled from the reactor itself (it's entirely possible to use sterling engines or thermocouples too) and any steam explosion is just that - a steam explosion
The fact that you can get hot side temps of 700-1400C means that the heat can be used directly in various industrial processes (eg: at ~1200C, water can be cracked to produce hydrogen, then air + plain old Haber–Bosch methods make ammonia from that and end products range from plastics to fertilizer).
Guard those "waste" piles well. They will be useful in the future.