Going to try to do a little service work here for Millz as this is hands down the best CR for shadow priests and routinely performs wonderfully for me. Think I've posted in this thread twice and this is not a solicited post but I just feel it's deserved for the amount of works that's been put into this CR (no offense to TuanHA but this is miles ahead of any of the TuanHA CR's I've used on other toons).
First,
recommendations for Teir 7 CoP option for each Highmaul fight is below (only for the difficulties that I've completed).
Kargath Normal and Heroic = CoP DoT Weave
Kargath Mythic = CoP Lite (try to make sure you keep both SW

and VT up on Kargath while DPS'ing the tigers, may not happen with the default CR if you don't switch targets). Be sure to be running Power Infusion/Insanity here as well.
Butcher Normal and Heroic = CoP DoT Weave. Once again, Power Infusion/Insanity.
Brackenspore Normal and Heroic = CoP Standard (I find standard to be best here for bursting Spore Shooters, otherwise you waste DPS getting dots up on them, you may try CoP Lite but I haven't had as much success with it here). Change to Twist of Fate and Insanity.
Tectus Normal and Heroic = CoP Lite, hands down rapes face here, if you're using anything else, you're doing it wrong. Use Twist of Fate and Insanity.
Twins Normal and Heroic = CoP Standard (Lite for Mythic I would think). Use Power Infusion and Insanity
Ko'ragh Normal and Heroic = CoP Standard. I prefer Twist of Fate and Insanity but Power Infusion may actually be really really close here.
Imperator Normal and Heroic = CoP Lite (I know right? Seems weird considering you will waste loads of dps on arcane aberrations, this is true, and depending on your raid group, CoP Standard may be better for the burst on aberrations. My guild has really good burst from melee on the aberrations, they die fast, I simply ignore them during P1-2 and help during P3 if needed. CoP Lite provides better cleave DPS for the Warmages and the P4 transition of the Warmages + Reaver). Twist of Fate and Insanity all day.
Overall, pulled the highest dps for me hands down to the immense amount of movement in this fight. Sadly your burst at the start looks like shit, BUT:
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The Link to Tectus right there I think says it all...That was a 7 minute 30 second heroic kill that took place this evening INCLUDING getting Crystalline Barrage 3 times. The Bracket % (far right) is basically a percentage ranking based on gear. I could link similar results from every other encounter in Highmaul, unfortunately, I'm lazy.
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The Basics
Basically, I'm spec'd for:
Desperate Prayer, Body and Soul, Insanity (always), (teir 4 doesn't matter), Twist of Fate or Power Infusion, Halo, Clarity of Power.
I use Vampiric Embrace manually based on when I think the raid needs it, had it set @ 10 players below 75% which seemed good for awhile, but prefer to save it so I don't overlap when a tranquility or healing tide goes out.
I also use healing tonics instead of healthstones at all times.
As far as gear is concerned, I consider optimal gear to be CoP Standard gear (mastery/multistrike). Unbuffed @ ilvl 662 I'm now sitting on 9.95% crit, 14.48% haste, 44.93% mastery, 20.89% Multistrike, 0.6% Versatility.
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Other things to note that will have an effect on your DPS:
1.) Movement - Always disable Honorbuddy/CR based movement. Movement should be done manually to avoid it clipping spells for 6 inch movement due to range. Also, always be sure to STRAFE rather than turning and moving whenever possible. Strafing will allow the bot to continue casting your instant cast spells during movement.
2.) Latency/FPS - I experience a significant drop in DPS anytime my latency exceeds 100ms or FPS drops below 12. (I run on a shitty old desktop with crapcastic cable...)
3.) Bad RNG/Mechanics - A rough patch of Crystalline Barrage on Tectus or having to perform stack swaps on butcher, carry flame thrower on Brack, bad fire on Twins, absorbing overflowing energy on Ko'ragh, being the branded guy on Imperator, will also drop your DPS an non-insignificant amount.
4.) Kill Strategy - Some guilds use a more conservative 'easier' kill strategy on boss fights than others. Sometimes this forces more movement and can cause your DPS to be sub-par.
5.) Healing/Raid Assist/Shield on Movement - Assisting the raid with emergency heals, shields, or shielding yourself during movement or at lower health will also account for a DPS loss. This doesn't mean don't do it, just know that you won't perform maximum DPS. Sadly, not all of us have amazing healers and sometimes this is needed.
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I've also gone ahead and
attached my configuration files that I use for each of these fights. I simply, class config/load profile each time we're moving from boss to boss killing trash.
Any questions, feel free to PM or respond here and I'll reply when I can.