Hey,
Wipes are tough to analyze so I'll focus on Zakuun. I've said it lots of times before in all different places, but I'll say it again here: don't beat yourself up about rankings and especially iLvl%.
Take a look at the rankings on heroic Zakuun for your iLvl. You have to go a really, really, really long way down that list to find a parse in which the duration was more than 4-minutes (ie. Your kill time was 4-min+). All of the top parses are sub-3-minutes and even a few less than 2-minutes. If you take a look at the top parse for your iLvl (Kevwl ~94K) - they cast lust on the pull and he even had a few 740 players in the group providing a bit of a boost. That's going to inflate his DPS immensely because he's able to provide a good opening burst and doesn't have as long to sustain it until the boss is dead. Long story short, there's examples like this everywhere in the rankings so don't even worry about them.
Looking specifically at your kill, there's a few things you can improve:
1. Haunting Spirits to 100%. It dropped off very shortly two times. The class trinket really helps smooth out shard regeneration so this will become easier with some better gear. You did pretty well but getting this to 100% makes a difference.
2. Lining up your cooldowns. You chose to use your Doomguard on pull, which would have been good if you guys used Lust on pull, but I would have saved it for when you actually used BL, which also would have dealt more damage since the boss was in execute for the Doomguard. Further, you should have saved a charge of Dark Soul for that Bloodlust+Doomguard combo and also used your 2nd potion there. You could have done much more DPS in that final phase if you lined up all those cooldowns.
To answer your question, on a fight like Tyrant, in order to maximize your DPS, you want to have both targets with full DoTs + Haunt and fill with Drain Soul when you have no DoTs to refresh. A further efficiency is to use the Glyph of Soul Swap and time that properly for the new add spawns, and all of this is going to be highly dependent on Shards because most of all you want to maintain Haunting Spirits so you have to have your 2 Shards every ~30s (and I personally don't feel your gear supports this play). A compromise would be to just hardcast your DoTs on the new target and Drain Soul whichever target needs extra damage. Save your Shards for SB:Haunt. Point being, you want both targets DoTted ~100%.