If your looking for an appropriate time period have you considered having the player enter into this world just shortly before *SPOILERS BELOW* Alduin is set adrift in time. That way you could structure the plot to alow the player to witness Alduin interact with all of his priests one last time before he flies off to fight Gormlaith Golden-Hilt, Felldir the Old and Hakon One-Eye; while at the same time preventing the player from fighting Alduin again and potentially erasing the events of Skyrim. You could use a situation like this to both explain why all of the masks were on there pedestal at the time of the players entrance by saying its a ritual facet of the priests' interaction with their dragon overlord. Going from there its not a huge stretch to say that when Alduin dosn't return from High Hrothgar the priests would get worried, and in short time the cult would fall into a state of turmoil; Leaving plenty of opportunities for the Dragonborn to slip into their ranks. In this situation it Paarthanax would have already founded the begginings of the Grey Beards and as such would be an enemy to the dragon cult. The heros Felldir the Old and Hakon One-Eye will still be alive, and will most likely be found attacking the dragon cult head on. I'm not completely sure if the time period is correct but I feel like Talos should be alive during this time period as well, and if he is then he and his followers would also be opposed to the Dragon Cult. The Akaviri would also be alive and at this time and definitely out to kill some Dragons. There would also be a rebel army involved with Lord Harrod and Skom Snow-Strider (the general who was responsible for the mass suicide at Forelhost). This could ocur between 1E110- 1E130 if Skom's Journal is a good date marker for the Defeat of the Dragon Cult.