Grid storage doesn't have the same weight limitations that EVs do, which opens up a lot more paths. Flow batteries, for one, might be all we need. They're already gearing those up for mass production, so we don't need any further breakthroughs (though they're always nice if they come).
Getting to 95% is surprisingly easy; there are non-linear factors at work to getting that last 5%, but you wouldn't need to use other sources very much at all. The wind often blows when the sun doesn't shine. We have tons of historical weather data about how these two combine in a given region, which means we can calculate the maximum expected lull between the two. Double that amount and put in enough storage to cover it. This basic plan was simulated in Australia, and it gets there for an affordable cost.
Then we can worry about that last 5%.
Nuclear advocates have been using the same talking points since the 90s, and have missed how the economics have been swept out from underneath them.