Did you really pick the figure from the RBMK reactor type?
For PWRs, 250 mÂł of LILW per GW annum is 28.5 mÂł of LILW per TWh.
2.5 million turkeys in a 2.4 kW oven for 3.5 hours uses 0.021 TWh.
So 2.5 million turkeys and 0.6 mÂł total low and intermediate wastes generated. Most of this can be released after ~300 years with negligible activity over natural background. That is a long time but not "basically forever".
They're talking about recycling the fuel and putting it back into the reactors. Unfortunately it's cheaper to mine fresh fuel than to reprocess used fuel ... as long as you just ignore the waste problem.
The source for that number is the International Atomic Energy Agency aka the nuclear control agency.
As for the rest of your ideas, its sadly not that easy. It has to be stored somewhere where it cant contaminate the environment, water cant get to it, tectonics are stable, etc. No permanent storage location for the waste has been found, to date.
And to burn the unburned fuel you would have to breed the material, which is a process that requires the most dangerous reactors and is extremely costly.
to burn the unburned fuel you would have to breed the material
France reprocesses spent fuel. With increased scale it would be cheaper and cut down on the volume of waste that must be dealt with regardless of if there's a nuclear industry in the future.
Breeding from non-fissile material is different to reprocessing though. Reprocessing is a chemical process, not a nuclear one. The UK had an operational reprocessing capability - though it is being decommissioned now because it wasn't cost effective with such a small fleet. Japan is still trying to bring its reprocessing plant online (after years of trouble). However France is doing it routinely for their domestic fleet and some foreign reactors IIRC. The USA made reprocessing illegal back in 1977 due to proliferation concerns. Despite that ban being repealed, they haven't set up the regulatory infrastructure to be able to do it so no one has bothered. Maybe the new nuclear industry will shake that up a bit.