I would think it's a much wider question, as Paul's description is extremely wide, covering myriad examples of choosing -- can God still attribute blame on people if God is doing the hardening? This is similar to the very wide hypothetical question Paul asks in the start of Romans 3.
I'd invite you to take a look at Romans 11:28-29.
As regards the gospel, they are enemies of God for your sake. But as regards election, they are beloved for the sake of their forefathers. For the gifts and the calling of God are irrevocable.
It's not easy to navigate this verse from any view, but it's definitely saying some of the hardening in Israel occurred for the sake of bringing in Gentiles, but regarding election they're beloved.
And in fact, y'hafta put the entirety of Romans 11:11ff in that context, because Paul explicitly states that this hardening is not to the point of falling:
So I ask, did they stumble in order that they might fall? By no means! Rather through their trespass salvation has come to the Gentiles, so as to make Israel jealous.
So here the issue isn't gaining or losing your salvation -- it's gaining or losing what they were seeking -- righteousness -- and that required God's mercy to receive. To flout those things that are also required -- faith, for instance -- would defy God's mercy a different way and cut you off at a tighter core. But of course it definitely does require continuance in faith -- perseverance in faith -- for those who have yet received God's mercy. Losing that faith definitely does cut you off from God's mercy.
I've few qualms about saying that people who are in church and who have fervor and strong emotions and deep convictions even, may yet drop out of their faith. We stand on the same grounds of faith, grace, and God's choosing that the Jewish people do. It works the same. Our hardness of heart can occur at different levels, and that hardness can thwart our attaining God's righteousness. God's mercy is thus required to soften our hearts, and not harden our hearts.
On which we'd agree. However, we disagree on what that very good basis is.
You're saying this is the reason why God hardened Israel. But put in context, that's not what Paul said. Paul said it's the reason
why he's praying that they might be saved. Israel has zeal, but it's wrongly placed, and so they didn't submit to God's righteousness. They need to be saved.
Brothers, my heart’s desire and prayer to God for them is that they may be saved. 2For I bear them witness that they have a zeal for God, but not according to knowledge. 3For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God’s righteousness.