Welcome to any and all corrections- I'm spinning this off the top of my head from what I've read, so I could be misremembering some stuff.
My current going theory is that Dyatlov suffered a violent schizophrenic break that lead to the group abandoning the tent and their eventual demise. It's the only thing I can come up with that answers some seemingly at odds facts (them leaving without shoes, but in an orderly fashion, etc).
First, a piece of cultural context that drove the development of this theory.
1.) At the time, and in large extent to this day, mental illness in Russia is a taboo and even shameful subject. Had Dyatlov been experiencing a slow decline, neither he nor those around him would have had the knowledge to pick up on it; in fact, they may have just ascribed any eccentricity to his 'stalwart' and strict character. Schizophrenia in particular can be a creeping disorder that even those around the schizophrenic sufferer may not notice; it often develops into a full blown illness under extreme stress and right around the mid 20s.
I believe a schizophrenic explanation also accounts for the government's weirdly close-lipped account and awkward handling of the case; at the time, in the Soviet Union, mental illness was often used as an excuse to imprison the politically inconvenient. Soviet investigators would probably not have even approached the topic, since good Soviet youth (as all the Dyatlov team members were, no moreso than Dyatlov himself) never, ever got schizophrenia (this ties into the Soviet belief that they were creating a "new man" free from things like mental illness, and that many mental disorders were simply the effect of oppression under capitalism, etc.)
On to my best attempt at a blow-by-blow account of what happened.
Schizophrenia may present in different forms and it is often exacerbated by stress; in Dyatlov's case, a couple of different incidents prior to the final hiking trip hint at this. His bizarre, strict "wash your feet" policy, is one item that stands out (perhaps he had a fear of pathogens). That he had previously given fellow hikers the silent treatment when they refused to obey his orders, and even started a hunger strike for the same reasons, indicate an already suspicious amount of paranoia and desire to exert control (infamously, untreated schizophrenics can starve to death because of their delusions- check out the harrowing documentary God Knows Where I Am).
Much was riding on this trip for Dyatlov. He was leading a group of eight other people (themselves experienced outdoorsmen), one of whom was significantly older and a WWII veteran, in an attempt to gain a master sportsman certification. The area was exceedingly remote, as well.
I think circumstantial evidence points to Dyatlov beginning to crack under the strain at least from the day before the team died. They left extremely late that day- 10 am- and when they set up their tent, it was in an odd manner (with ski poles instead of stakes, iirc), and in an odd location (why not closer to the tree line, where they would be sheltered from wind).
We know from prior accounts that Dyatlov was a strict, commanding leader. His team would likely have been following his orders-- from the late start, to the odd set up, to the odd location. I believe that Dyatlov was suffering disordered and paranoid thinking by this point, which is typical of schizophrenics; they'll do strange things or alter their normal behavior in order to confound those "pursuing" them in their delusions.
At this point, as they began to settle in, I think someone confronted him. Perhaps Zolotaryov, who certainly had the experience and age to realize that something wasn't quite right (this may also explain why he and Thibo had remained dressed). This argument rapidly brought Dyatlov to his boiling point, and he snapped- ordering them out of the tent immediately and in a bizarre fashion (ie cutting through it rather than exiting normally, suggesting some sort of irrational paranoia about the regular exit). Perhaps he held the missing knife on them, and perhaps the team, too young and too enamored of their leader (with the exception of Zolotaryov) to resist, followed his orders, thinking he'd quickly come to his senses in the cold.
The team headed to the tree line, where Dyatlov ordered Doroshenko and Krivonischenko to make a fire and to create a sort of "duck blind" from the cedar so they would watch the tent (again, a symptom of paranoia; perhaps he believed something dangerous was within the tent and hunting for them). Eventually, they built a fire, but by that time, Doroshenko and Krivonischenko were dying of hypothermia, having exerted themselves gathering wood (getting sweaty) and then that sweat freezing. They lay close to the fire as possible (leading to the superficial burns seen on their bodies), but in the end, succumbed. Perhaps Dyatlov, still in charge and paranoid, ordered the team to flip Doroshenko so he could not "see" Dyatlov (the fear of being watched or judged is extreme with schizophrenia).
At this point, I think Zolotaryov finally took action. They stripped the dead for their clothes, and then he and the others bound a violently-resisting Dyatlov (which explains the symmetrical abrasions on Dyatlov's ankles) and left him. Perhaps Zina and Rustem stayed behind, unwilling to leave their friend and leader. Exhausted and reasoning that they'd only survive an attempt to get back in the tent come morning, Zolotaryov lead the remaining three members to a ravine, where they worked to construct a snow shelter.
At some point, Dyatlov either wiggled free or got Zina and Rustem to untie him. He then, deeply paranoid, hunted down an exhausted Zolotaryov and his group, killing them rapidly and in short succession with a blunt object (possibly a rock)? He then lead Zina and Rustem back towards the tent; I think here Rustem finally may have snapped and fought Dyatlov, and shortly after, they all perished from exhaustion and exposure.
Some things I can't account for:
1.) The weird camera on Zolotaryov's neck.
2.) Zolotaryov's group all died of extreme trauma and very close together (almost as if they were struck while asleep) and I do question that a man suffering from the effects of extreme exposure could have done it (although there's something to be said for the strength of someone dangerously mentally ill).
3.) Why did Zina and Rustem (Rustem specifically, since he was so experienced) stick with Dyatlov for so long in this potential scenario?
So... give me your thoughts!