Assuming someone more ruthless within the SS doesn't beat them to the punch. Secret police officers have astonishingly short life expectancies in police states when the dictators protecting them are removed from office. Most of the Nazi leadership loathed Himmler much like how most of Stalin's Politburo felt about Beria and looking at how long the NKVD chief lasted post-Stalin I wouldn't give Himmler any better odds.
Himmler was partially relieved when Heydrich died, you know. Heydrich could have probably beaten him in everything, and I don't put it beyond him to off Himmler if he could.
EXACTLY. Bormann faces similar problems in having great, GREAT power(I'd say stronger than anybody at a certain point), but it being utterly Hitler-dependent and in exchange for earning the loathing of the rest of the Nazi hierarchy. Though interestingly, Stalin had a position nebulously like Bormann in Lenin's last days*, and also had a similar MO and personality**. But that was a bureaucratic system that had time to develop without war post 1920, and Stalin could outmanuever his flashier rivals. Germany was also a different system, with different players.
There aren't enough WIs about Bormann. His influence on Hitler during the war was a national disaster, like Speer said.
** A rather boorish, crude bureaucrat that was dismissed and loathed by more cultured, charismatic ideologue rivals, and partially rose to power because he was underestimated. However, what they lacked in grace, they more than made up in bureaucratic intrigue and meticulousness.