So this was actually the first build I was able to get "going" when S3 went live due to some very weird luck with my RNG. My hexing pants were abysmal (ty smartloot for giving me an int pair with armor and life regen), but I was able to make one little change to make this build completely faceroll in T6: Goldwrap. This belt, when combined with avarice band + boon of the hoarder, makes you damn near invincible... if you can keep the buff up. In dense rifts you don't need to try at all, but if you encounter sparse rifts and your toughness is naturally low, you have to be very careful.
In order to keep my hatred up, I had to roll hatred per sec on my offhand (a K'mar Tenclip until I can get a calamity) and my chest. Additionally, I had to use hexing pants (when the buff is active, it improves hatred/s effects including the archery bonus for offhand hand crossbows). While I'm not quite hatred neutral, I'm damn near close.
You guys might now about the T6 Rift Clearing Competition, which is a friendly competition to see which class is best at speedfarming T6. You can find a thread both on the official forums and here on Diablofans (the latter seems outdated at this point though).
1. Clear 10 subsequent T6 Rifts.
2. Pick up legendaries and (attempt to) kill goblins.
With some more experimentation going into this build recently, a few things have changed. If you are getting close to the high-end, I think it's even better to use F+R and drop any resource items altogether. I also used Wreath of Lightning instead of another dps gem, the damage boost from the rings is more than enough, I wasn't even using a Hellfire amulet and only had one ancient weapon. The guide will be updated to reflect this. This build is strong enough to solo farm rifts in 4-player parties at almost the same speed (maybe +10 seconds per run), I was doing this while others were clearing bounties and told them when to join to leech the RG.
Here is my contribution, which posted there already as well:
Build: Natalya Strafe
Total Time: 21:17
Video is sped up 2x. Sub 20 minutes on average is definitely possible with this. My items still have lots of room for improvement, but probably having a better PC would have easily been enough to cut 1-2 minutes in loading times (averaging more or less 3-8 seconds per zone change for me). First rift starts at 00:26, last reward from Orek received at 11:05 - 21min 17sec. (For actual in-game speed, just watch at 0.5x speed, it also has some fun effects on the music.)