1) week storage and 3-6 months storage are extreme events, similar in probability as overlapping technical shutdowns in nuclear facilities. In practice, with interconnection, it is even arguable that such long term storage are even needed.
2) the technology built for short term storage is usually not that bad for medium term storage either. In any case, if you want a nuclear grid, you will need to invest in storage technology, and there is no reason the progress in those technology will only improve short term storage solutions.
But I 100% agree: a nuclear plant turned on during winter will help. I'm not against nuclear, I just want to react to the incorrect view that storage is just a renewable problem.
NG backup works fine, and will continue working fine indefinitely. Storage cuts the fraction of time the furnace needs to run.
Eventually, synthetic fuel will displace NG. It will be imported at need, same as NG today, but with no possibility of cartels.
If you can turn a nuclear plant off (summer) and on (winter) once a year, the storage requirement for solar drops by a lot.