You're not just coming here and asking people to play your character for you. (Some people do that!) You've done the work to figure things out on your own and are still having trouble. I respect that, but this thread isn't a place to give or receive individual play and gear advice. With only a few exceptions, requests for personalized help are strictly forbidden on these forums.
The "simple questions" thread is a more appropriate place to ask your questions, rule 7 is suspended there. I'll move your post there for you; in the future, please post in the right place.
Also, if your shaman is your main character, update your profile to show that. Then you won't have to include your armory link in your post.
My shaman is pretty geared from weeks & weeks of 8/8 10m reg DS, i.e, 4pc T13. I do all the things in a fight you'd expect: I keep HR down. I keep ES & a ticking Riptide on a tank. I cast a couple CH & Riptide anybody who needs a quick heal, or one of my 'Likely Suspects' dps. Rinse & repeat, bolts for mana as needed. I loose an occasional UE for the cheap instant bump & free CH power-up, if a CH is needed in that window of time. I'm just not getting the kind of HPS I should have at this point in my gear. I'm a shaky 15-16k healer & starting to hold my guild back from HM's.
On meters I get smoked by virtually *everybody* who heals on a given fight. Our Holy pally is freakish; geared, highly skilled & of Blizz' current darling class/spec. 30k HPS consistently. Fine... but our Shadow priests go Disc & out-heal me. Our bear goes Resto & out-heals me. I go into LFR even, and have to work really hard to beat other shamans who're far less geared. I check Recount and see no glaring disparities between our cast selection & quantity thereof. I've pored over these & other forums like a person possessed. I've tried every secondary-stat gearing/reforging strategy that made any sense to me - and some that didn't, to no avail.
Anyone have some ideas?