Keep srs rolling on the boss (it's not padding.. boss needs to be low on hp by the end or you won't meet the enrage).. and just game your multi shots.. keep aoe'ing when you can.. and when you're single targeting, when trinkets proc.. multi shot once and let the buffed srs roll on everything.. then continue to single target..
biggest thing from your logs that I can see is that you seem to just keep switching off the targets before they're dead.. i.e. not kill shotting.. that's a big loss in dps.. kill shot everything you can mang.. as you said, the key adds on each gate need to die quick.. so stay on them till they're dead and kill shot them.. most of your 7+ minute attempts you only had like 2-4 kill shots total..
and your barrage dmg seems low too.. you might wanna delay it a bit and not use it when there are only 1 or 2 adds up.. make sure to use it at optimal times