remnants and rejections

Romans 11:1-10

The key words in this passage are reject, remnant, chosen and elect. Paul contrasts grace and works, showing them to be opposites: if salvation is by works at all then it is not by grace at all. Paul is arguing that God has not completely rejected Israel: he is evidence that there are some Israelites who believe. This matches God's pattern: he has always preserved a remnant of the nation to remain close to him. Paul argues for God's sovereign choice and grace in this: that God chose certain members of the nation, in grace, to remain in him while he chose to harden other members of the nation.
This shows me that God is sovereign and beyond my understanding. I can't entirely see how he can be just when he chooses some to have the ability to respond to him and chooses to harden others. I know that some people will say that God only chooses for grace and that it is not that he chooses others for destruction but just that he doesn't choose them for grace. First, I think that it splitting hairs and, secondly, that's not what Romans 11:7-8 say. This I am convinced of: the judge of all the earth will do right.