To really understand this passage lets work backwards
The phrase "arouse them to jealousy" leads me to consider the nature of jealousy.
Jealousy by Definition
An unhappy or angry feeling of wanting to have what someone else has.
Now through this definition we can see that this means that someone else will have what they want. Lets look back to the passage to find out what this is:
"the salvation is to the nations"
The passage shows us that what they will want is the salvation that is to the nations. This makes sense considering that the salvation did belong to them to begin with.
The Parable of the Cake
A parent offers a piece of cake to a child, then after the child refuses, the cake was given to the little brother in hopes that jealousy will arise and cause both to want to eat the cake. Whereas the the older child metaphors to the Jews, the younger child metaphors to the Gentiles, and the cake metaphors to the salvation.
"but by their fall"
Looking back to the Parable of the Cake we see that the older brother refused to take the cake. This was against the wishes of the parent, therefore in similarity a transgression or a falling away from the desire of the parent. The Jews did this by refusing the message of salvation. Yet it was by their refusal to "eat the cake" that the younger brother got a chance to eat some ^^,
"Did they stumble that they might fall? let it not be!"
God who is the best parent ever planned it that the Jews would "refuse the cake" because he loves his gentiles to.
What then? What Israel is seeking, it has not obtained, but those who were chosen obtained it, and the rest were hardened (Romans 11:7 NASB)
Some added correction for the growth of the questioner
Question: "Paul makes the rather absurd claim that the Jews were not tripped up by God simply so He could watch them fall, but rather to instill jealousy in the gentiles:"
Paul gives the reason that the hearts where hardened for the Jews:
But what is the divine response to him? “I have kept for Myself seven thousand men who have not bowed the knee to Baal.” (Romans 11:4 NASB)
Therefore we can see that the reason Paul offers for the hardened hearts of those Jews came from their Baal worship.
Question: "Why would the gentiles be jealous that God stuck an obstacle, for tripping over, in the path of the Jews?"
It's designed that the Jews would go to jealousy over the Gentiles salvation.
In Question: "that the Jews refused to abandon Torah" (edited slightly)
Salvation requires the abandonment of the "Law that causes curses" and attachment to the "Law that causes grace" yet both defined in the Torah.
- "Law that causes grace" (Ten Commandments)
- "Law that causes curses" - Exodus 21 +
Why two sets of Laws?
The second set of laws where the punishment for the Israelite's worshiping the calf at the bottom of the mountain while the ten commandments where given.
Therefore instead of abandoning the Torah, they only have to abandon the curse.
The Last Question
"Is Romans 11:11 a form of hyperbole or does he really want us to understand that the Jews' dismissal of Jesus as their Messiah was part of a divine scheme to woo gentiles?"
God understands all things, and he was the one that hardened their hearts. He also will be the one to soften their hearts to realize the salvation. That this became true:
As He says also in Hosea, “I will call those who were not My people, ‘My people,’ And her who was not beloved, ‘beloved.’” (Romans 9:25 NASB)
For clarity it was God's plan, it happened, therefore part of his plan.