Mystery Solved?

Part 1 Chaper 7:
Yeah, so Holmes was very laid back in the last chapter while he was listening to Lestrade's and Gregson's conclusions. Holmes has Lestrade offer his conclusion. Lestrade finds a case of pills in Joseph Stangerson's hotel room at the time of his death. Holmes cries out, "The last link, my case is complete." So apparently, Holmes wanted to seem very calm and relaxed until the other detectives revealed their errors, and then bam, he tells them that he's solved the case. I'm beginning to view Holmes as a perfectionist. He wants to be the person who solves the mystery and only him.
Holmes tests the pills by cutting one in half and feeding it to the servant's dog. The following passage will reveal more about Holmes:
"Holmes had taken out his watch, and as minute foloowed minute without result, an expression of the utmost chagrin and disappointment appeared upon his features. He gnawed his lip, drummed his fingers upon the table, and showed every other symptom of acute impatience. So great was his emotion that I felt sincerely sorry for him, while the two detectives smiled derisively, by no means displeased at this check which he had met. "It can't be a coincidence," he cried, at last springing from his chair and pacing wildly up and down the room; "it is impossible that it should be a mere coincidence. The very pills which I suspected in the case of Drebber are actually found after the death of Stangerson. And yet they are inert. What can it mean? Surely my whole chain of reasoning cannot have been false. It is impossible!" (49).
Holmes is very impatient and he just doesn't like to be proved wrong. He's definitely a perfectionist. In this passage, he seems almost bipolar because he is crazily questioning his own thought process and almost punishing himself for being wrong. Holmes even knows who the assassin is already. He doesn't reveal the name to Lestrade and Gregson when they ask him, but he tells them that they have to take it step by step in arresting him.
The murderer was Jefferson Hope and he was the cab driver, I think, because Holmes had Hope bring up a cab and asked Hope to transport his bags. Then he arrests Hope.

Part 2 Chapters 1-4
These chapters don't include Sherlock Holmes. I think they're explaining why Hope murders Enoch Drebber and Joseph Staggerson. For example, John Ferrier and his adopted daughter, Lucy Ferrier, were about to die in the desert when a caravan of wagons rescued them. The leader of the Mormons, Brigham Young demanded that Ferrier adopt their beliefs in return for their rescue. Lucy grows up and falls in love with a christian man, name Jefferson Hope. Young finds out and demands that Ferrier have his daughter choose young Drebber or Stangerson as the husband for Lucy. Hope comes back and helps them get out of the land of the saints.