Trinket wise your going to want to either convince your team to go kill gorefiend to get a mythic UeH or your going to want to go do heroic gorefiend for one. It's a massive gain for unholy and a trinket that I use on almost every fight.
Also, if you plan to use UH on more fights, your going to want to grab a Vial of Convulsive Shadows from Iron Maidens for ST/BoS fights. This can be replaced by a Grontooth Warhorn (the Mythic dungeon heirloom trinket) for demon fights but is still highly suggested for many fights.
As for when to use each trinket/talent and on what boss, I posted a trinket list a few pages ago but here is updated one:
Iron Reaver: BoS, UeH/Vial
Kormrok: BoS, UeH/Vial
Council: NP, UeH/DC, or BoS, UeH/Vial
Killrog: BoS, UeH/Vial
Gorefiend: NP, UeH/Class, or BoS, UeH/Vial
Iskar: NP, UeH/DC
Socrathar: BoS, UeH/Vial
Tyrant: BoS, UeH/Vial, I've seen good results with Grontooth also.
Zakuun: BoS, UeH/Vial, same as Tyrant about Grontooth.
Xhul: NP, UeH/DC
Manno: NP, UeH/Grontooth, DC can also work but I've found it to be a bit worse. BoS, UeH/Vial, depends on AoE/Kill Speed.
Archie: NP, UeH/Grontooth, or BoS, UeH/Vial
This does also partial depend on you raid group/comp, how much AoE you have, and how fast you are killing a bosses, but these are pretty balanced choices.
Xhul - Mostly based on Jan 20th kill (your best)
Your running the Class trinket and Pebble, if you can't get your hands on a UeH I think you best bet would be the class trinket and your DC.
As you guessed, your NP uptime is a bit spotty, commonly dropping off early. This is the biggest problem I see. There is a nice addon called Compact Runes, it is a basic rune tracker with a lot of nice build in modules for DKs, including a festering strike tracker. I'll see if I can dig up a WA that does this also a bit later....
Your dark transformation uptime was a bit low, 74%, aim for closer to 80ish.
I see that your on the blackhole soaking team at least for the final phase. Unless you might be sent into earlier one, save your AMS for mid felsurge cast and if you are chosen you will immune it and make less fire for your raid.
Your ring hits are really REALLY low, I checked your armory and your ring isn't maxed out yet, try to do this ASAP by throwing valor into it.
I'm guessing your enchants/gems where still mastery for this fight? If so your going to be losing out on a lot of necrosis damage.
Soul Reaper Usage is a bit low, but better than a lot.
Manno - Mostly based on Feb 4th Kill
Again you are using the Class Trinket but this time pared with the Grontooth Warhorn. Your group as a insane amount of AoE (Warrior, Ench, Ele, Warlock, Combat Rogue...) that your damage to the imps is going to minimal so the usefulness of the class trinket is going to diminish. GET A UEH!!
You can Dark Sim the imps if they stay up for a while. It gives you a 400k fireball that does AoE damage so if some imps are still up you can get HUGE hits. (1.5mil is my record)
Your NP is still dropping off a bit early, but better than on Xhul.
Could get a few more SRs, doom lords are great targets for them.
You hardly touched the infernals, make sure you get your NP ticking on them quickly for a nice damage boost, can also be easy kills to proc the Warhorn off of.
Throw some DnD's down for infernals or imps.
That should cover at least some of it.