Seems to me that Rand's model is similar to LessWrong's "rationality as non-self-destruction".

Objectivism in the novels doesn't give the heroes any positive powers. It merely helps them avoid some harmful beliefs and behaviors, which are extremely common. Not burdened by these negative beliefs and behaviors, these "normal men" can fully focus on what they are good at, and if they have high intelligence and make the right choices, they can achieve impressive results.

(The harmful beliefs and behaviors include: feeling guilty for being good at something, focusing on exploiting other people instead of developing one's own skills.)

Hank Rearden's design of a new railroad bridge was completely unrelated to his political beliefs. It was a consequence of his natural talent and hard work, perhaps some luck. The political beliefs only influenced his decision of what to do with the invented technology. I don't remember what exactly were his options, but I think one of them was "archive the technology, to prevent changes in the industry, to preserve existing social order", and as a consequence of his beliefs he refused to consider this option. And even this was before he became a full Objectivist. (The only perfect Objectivist in the novel is Galt; and perhaps the people who later accept Galt's views.)

Francisco d'Anconia's fortune, as you wrote, was inherited. That's a random factor, unrelated to Objectivism.

John Galt's "magical" motor was also a result of his natural talent and hard work, plus some luck. The political beliefs only influenced his decision to hide the motor from public, using a private investor and a secret place.

Violating the law of thermodynamics, and surviving the torture without damage... that's fairy-tale stuff. But I think none of them is an in-universe consequence of Objectivism.

So, what exactly does Objectivism (or Hank Rearden's beliefs, which are partial Objectivism plus some compartmentalization) cause, in-universe?

It makes the heroes focus on their technical skills, and the more enlightened heroes on keeping their technical inventions for themselves. As opposed to attempting a political carreer or serving the existing political powers. Instead of networking, Rearden focuses on studying metal. Instead of donating the magical machine to the government, Galt keeps it secret. Instead of having his fortune taken by government, d'Anconia destroys it... probably because of a lack of smarter alternative (or maybe he somehow secretly preserves a part of his fortune, and ostentatiously destroys the rest to draw away attention; I don't remember the details here).

Without Objectivism, the heroes would most likely become clueless nerds serving the elite, because they couldn't win at the political fight (requires a completely different set of skills that people like Mouch are experts in), but they also wouldn't understand that the system is intentionally designed against them, so they would spend their energy in a futile fight, winning a few battles but losing the war.

Understanding the system allows one to focus on finding an "out of the box" solution. John Galt's victory is his ability to use his natural talent and work to devise a solution where he can live without political masters. He is economically independent, thanks to his magical motor, but also mentally independent. (If we removed the magic, his victory would be understanding the system, and the ability to resist its emotional blackmail and optimize for himself.)

The lack of this understanding made Rearden vulnerable to blackmail from his wife, and in a way cost Eddie Willers his life. (And James Taggart his sanity, if I remember correctly.)

tl;dr: (According to Rand) Objectivism makes you able to understand how the system works, so you can more realistically optimize for your values. Objectivism doesn't give you talent, skills, or luck; but it gives you a chance to use them more efficiently, instead of wasting them in a fight you cannot win.

EDIT: In real life, I expect that an Objectivist training could make people be more aware of their goals and negotiate harder. Maybe increase work ethics.