While I'll be trying my very best to adapt and explain as many of the features from the game so that they can be transferred to the RP and still make some semblance of sense, I feel like some things are easier to explain than others, and a lot of things in Bloodborne can be theorized about just by extrapolating from other things we know more about. Some things, like the Doll or the Messengers, are so different from everything else that there isn't any real basis for even an educated guess. Sure, the Doll could be a Great One... but then why can the player kill other Great Ones, up to and including the Moon Presence, but not the Doll? The Doll might also just be a product of Gehrman's memories brought to life by the Moon Presence for the same reason as the Hunter's Dream was made to look like the Old Hunter Workshop: to make Gehrman more at ease. But if that was the case, why would the Doll retain that form after Gehrman died? And why would she remain even after the Moon Presence was destroyed?
Too few details to base a singular theory on, which is why we/I have a lot of freedom in what to make of them. Other things, not so much.
So let us base the theory on things we know. Great Ones can be killed, but not always, and their death is not always final. Amygdala can't die in Yharnam or Yahar'gul - in other words, in the "real" world - but when encountered in the Nightmare Frontier or the old labyrinth, it can die. Neither of these places are entirely within the real world, however; one is obviously in the nightmare, and the other is in a place between the real world and nightmares. So all Amygdala in the real world are indestructible, and all Amygdala in the nightmare can be killed. With this as the baseline, I'll posit that Great Ones can only be killed in nightmares.
Now let's look at evidence against this. All in all, only four Great Ones are encountered in the real world: Amygdala (which is invincible), Rom, Ebrietas and the Celestial Emissary... or rather, the areas they occupy are reached through the real world. Rom is the easiest one to cross off the list, as it seems pretty clear from context that when the player leaps off the Byrgenwerth platform and into the lake, they pass into another world where the laws of nature are different, a world that seems to exist inside the lake itself.
Ebrietas is a little harder, but there is still plenty of evidence that her cave isn't entirely within the domain of the real world. For one, the cave is reached through the upper cathedral - literally the topmost level of the building itself - by an elevator straight down, in a shaft that can't be seen from ground-level in any way. The cave also houses various ruins and statues, all of which seem far more ancient and of a different architecture from what is seen in Yharnam, and is home to the Altar of Despair, an object capable of actually reversing time. So we descend into an area that seems completely out of place compared to where we just came from, where the laws of nature are different; from this viewpoint there is an almost direct parallel between Ebrietas' lair and Rom's lake. Add to this the fact that Ebrietas is originally from the labyrinth and possesses a ritual chalice - an artifact that allows teleportation into the old labyrinth - and there's a lot of circumstantial evidence that Ebrietas isn't entirely in the real world either.
The Celestial Emissary is the hardest one to explain. It's a Kin Great One, supposedly helped to transcend through the lumenflowers of the garden it is found it (and which are prominently present at the home of the Living Failures, the prototypes of the Celestial Emissary), yet it is killed... right? Unlike Rom or Ebrietas, we never encounter the Celestial Emissary anywhere else, despite the fact that it should have been cast out of the area occupied by this manifestation of it and forced to venture elsewhere. This could be shrugged off with the argument that it might just have gone somewhere the player never gets to visit, of course, but I'd like to point out how the fight against the emissary begins: you fight a limitless horde of celestial minions, one of which is the emissary, identifiable solely by the fact that hitting it drains the boss' health bar. Until the player does enough damage to the emissary, it is identical to the minions sprouting from the ground around it; the same ground the emissary itself sprouts from at the start of the fight. So, I'd pose a question: what evidence do we have, aside from it getting bigger and the health bar naming it "Celestial Emissary", that what we are fighting is actually the emissary? My theory is that the player does fight an emissary, but that what we fight in the game isn't actually the Celestial Emissary. I don't think the Great One, Celestial Emissary, is ever killed, because I think the Great One isn't the little blue men. I think it's the lumenflowers spewing out minions, all of which are indestructible.
It's a stretch, I realize, but... yeah, I'm proving a point. Saying that circumstantial invincibility is due to gameplay limitations is probably correct, but that doesn't mean that there isn't an explanation.
Gehrman I'd go so far as to say is downright easy to explain, and I don't even need to theorize a whole lot to do so. I left out two creatures that can't be destroyed by ordinary means, of which only one is relevant here: Queen Annalise (who is a mystery in and by herself) and the player character. When the player "dies", they reawaken in the Hunter's Dream and get to reappear and try again. When you try to kill Gehrman before the boss-battle, he disappears only to reappear later.
Just before Gehrman's boss fight becomes available, the player has a choice: awaken from the Hunter's Dream by letting Gehrman kill you, or refuse and fight him. Accepting frees the player and, evidenced by Eileen and Djura, loses the ability to come back to life. If the player refuses, however, even being killed by Gehrman doesn't free the Hunter, leading one to believe that it is not the act of Gehrman killing the player that frees them, but rather the player wanting the dream to end, which is the trigger. Gehrman himself even says: "You must accept your death. Be freed from the night..." Unless you accept your death, you can't be free. It is also worth noting that this option only even comes up when the dream itself is in flames, clearly disintegrating now that your mission has been completed; only once you have completed the task set forth by the Moon Presence - to kill Mergo's Wet Nurse - are you allowed to go free.
Now Gehrman. Let's look at the conditions the player has to fulfill in order to be freed:
They must die. This is easy enough; the player kills Gehrman, so he's dead.
They must accept their death. One line of dialogue from Gehrman reads: "Oh, Laurence... Master Willem... Somebody help me... Unshackle me please, anybody... I've had enough of this dream... The night blocks all sight... Oh, somebody, please...", another, when offering the player the choice, reads "Good Hunter, you've done well, the night is near its end. Now I will show you mercy. You will die, forget the dream, and awake under the morning sun. You will be freed from this terrible Hunter's Dream. " and when he dies, he says "The night, and the dream, were long..." Together, this - to me, at least - certainly suggests that Gehrman wanted to be free from the dream. He wanted to die.
Finally, they must have completed the mission given to them by the Moon Presence. Gehrman is the caretaker of the Hunter's Dream and the "Hunter's helper"; the very purpose of him being in the dream is to guide Hunters to complete the tasks they are given by the Moon Presence. In other words: the player, by completing their own mission, inadvertently also completes Gehrman's. The player and Gehrman is in the same situation at that point, so the only thing that ultimately matters is whether the player accepts death or not.
Eh, this post turned out to be quite a bit longer than planned. There's certainly some interesting ideas in what you mentioned; I'll keep it in mind.
