I never understood why people put so much thought/effort into these things and then make choices I don't think make sense.
Opening Gate - Templar: Legendary Fatebringer
Like Fatebringer is probably the worst VoG primary for these parts, since the hand cannon nerfs make it less effective and faster firing guns have a huge advantage because of oracle disruptor. Since you're not really doing well on either count, I would stick with something that can easily hit things at range for the hobs and call it a day.
Lamp Section - Thrawlway: Genesis Chain
See, here I would consider using something like Fatebringer because it can one hit the thralls and do firefly damage. Because of the nerfs I still wouldn't use Fatebringer, but I imagine a scout with firefly would be more useful than Genesis Chain.
Deathsinger and Crota: Fatebringer, shotgun, Ghallahorn.
For Deathsinger I would totally go sword or Sleeper for quick kills. Either or these are much better than Gjallarhorn for Deathsinger. I also wouldn't use Fatebringer for the usual reasons and would stick with something at range to pick off the wizard, shrieker, knights, ogres, Deathsinger. Not to mention it helps more during Crota. Using Gjallarhorn for Crota is obviously fine.
Sisters - Oryx: Chaos Dogma (or high impact scout rifle w/ triple tap), Black Spindle, heavy of your choice (just anything that can take down the ogres fast. Machine guns seem to do the job really well)
Seriously, no Touch of Malice? It is the undisputed best weapon for the Daughters and you don't need something like Black Spindle for any part of Oryx. Any gun in that sniper archetype can one hit the Knight and something like Sleeper is better for Ogres. Not to mention Touch of Malice is really good for stunning Oryx.
Opening - Aksis Phase 1: Steel Medulla, Ex Machina, Ghallahorn (no need for Warpath here, because it sucks against Captains, and Vosik only has 1 crit-spot, unlike Aksis).
This is another time when I would stick with a sword. They melt captains quickly and easily and make things smoother. At the very least I would swap Gjallarhorn for Sleeper, since rockets make Vosik move like crazy and ultimately screw over snipers/Sleeper users.
Aksis Phase 2: Chaos Dogma, Black Spindle/Ice-Breaker, Warpath. Now that we don't have an exotic taking up our heavy slot, we can have any exotic secondary or primary we want. People were saying the Hezen Vengeance was good against Aksis, but I personally wasn't getting as good of numbers with it. But the Warpath is REALLY good against Aksis.
First off, Ice Breaker has awful DPS and is baffling considering you're going for the "best" DPS heavy. Maybe if you use it absolutely perfectly it is good, but odds are you'll do more damage with a high impact sniper than Ice Breaker.
As for Warpath, I still rather use a sword to kill Captains and do good damage. Too many people forget that DPS is important, but being able to stay alive, effectively do the other parts and so forth are much more important. The reason that DD SGA is on the front page is because Warpath might be able to out DPS DD, but DD is still a more functional weapon.