As it stands right now Customer Service has no ability to supply players with any gear. As far as I know the most they can do is offer some crafting materials, phoenix credits, and weapon skins.
A few days ago I was finishing a 3 phase heroic only to find after killing the last boss on the 3rd phase that there was a NPC stuck behind one of the doors it was meant to come out of. As a result we couldn't complete the heroic and all had to leave.
I provided proof to customer service with video evidence so it was blatantly obvious what happened and yet they were unable to give out anything other than some phoenix credits.
So my suggestion is give them the capability in cases like this offer a Supply drop to players.
It is only fair that if we cant complete something because of a game glitch that prevents us from getting gear...customer service should have the ability to make us whole via dropping a supply drop for us. At least until the game glitches are finished.
This would include players not getting loot at the end of a incursion, glitching out mid heroics and as a result not able to finish....or whatever other multiple glitches that can screw you out of gear.
We shouldn't lose out on 45 minutes of work due to a game glitch.
Since you appear to be doing 3 phase heroic I'm going to guess that your gs is above 240 if not capped. So with customer service giving you crafting materials it's pretty much the same as getting a supply drop. Would be willing to bet at this point of the game for you that you're just trying to min max. I the supply drop I got was a firecrest piece 229 lmg and a 229 chest, all 3 instant shards. They are just saving you the time from opening the chest, being disappointed and then sharding it.