In the short-term, gas backup for such scenarios (which are relatively rare, and during which renewables will still operate at some non-100% fraction of the required energy) seems like it might be a reasonable option: we could probably get to (pulling numbers out of thin air) 95% renewable generation or something that way.
Longer term, we'll definitely need some kind of long-term storage though. Perhaps synthetic fuel driven by overcapacity renewables during peak generation times might be an option here?