So this week I spent level my priest 81-85, bought the 377 blue pvp gear to do the new heroics, Managed to grab some gear through lfg and lucked my way into getting a few pieces while I did 8/8 DS lfr. As I continue to do heroics even with my new gear, while I admit not all enchants/gems are top end my dps still seems shitty. I unfortunately don't have any raid logs at the moment but I do like 25-26k in a heroic, which I could see if I was just playing incorrectly at this ilvl; but even running my gear through Simcraft seems to put me at 26.9k.
I guess I'm just trying to figure out what the issue is. Is shadow just that gear dependent or am I just ignorant about something. To be honest I guess I expected to be a little closer to my normal dps on my mage and dk that are in a little better, but similar gear.
The closest thing to a Patchwerk style fight in the current tier would be Ultraxion, so I guess you can just maximize things by making sure your DoTs will last the duration of being out of phase+cast time, or re-apply beforehand. I believe a Macro to Shadow Word; Death + Extra ActionButton could also help. Using Dispersion whilst you're phased out to ensure you don't waste as much time DPSing can also help, if you do need mana.
What do you expect to be doing with 377 blue PvP gear? I think 26K sounds not too shabby when you are in pretty awful gear. Not to mention that I have no idea what buffs were present for the encounters you were doing.
To give you some comparison, I don't get DI or 10% sp or 5% spell crit and I can do about 33 to 35K on ultraxion and I'm in 395. So if you're in 377, that seems roughly right.