i strive to find a use for demonic circle. I didnt go through all seven pages of the post, so im not sure if im missing key things/repeating information. sorry if i am.
flame leviathan: only vaguely useful, but can set you up with a place to meet your chopper (i get launched).
ignis: i play the role of backup for the shadowpriests. demonic circle is put in place so i can shatter the adds without having to stand always in range.
razorscale: i use it to teleport to the harpoons, as i click them for my guild
deconstructor: close to useless on normal, immensely helpful on hardmode. couple of ways to do this, put it in the middle to teleport you back after running out, or to exactly where you want to go for light bombs so its always at the correct range for the tank taunt
iron council: placing it outside the room can save your entire raid from a wipe. when a wipe is called, teleport out and run down the hall. When one of the guys chases you, it will reset the right
kolagarn: gets me across the room from eyebeams without wasting time running
auriya gets me back in front of the boss after fears
thorim gets me quickly out of the way of the lightning lines (and blizzard on hard mode)
hodir gets me across the room for a variety of reasons, whether chasing useful buffs or a flash freeze
freya gets me across the room to those pesky hard to reach trees, and away from acorns during phase 2
mimiron gets me away from inconvenient bomb bots when im tanking, and makes me run less during spinning up (careful not to range your healers)
vezax: gets me back into a shadowcrash if i screw it up, or across the room to saronite vapors, or out of the raid for life drain
yogg: gets you away from clouds back to the front of the room, and around the head for phase 2 and the beginning of 3.