Grouping with friends and doing split bounties is going to make your effort to gain extraction mats much quicker, as I'm sure you already know. However, a lot of people aren't aware of how the current Bonus Bounty situation is working.
ALWAYS do the Bonus bounty map (act) first. After you finish that, the bonus moves to another map (act), and then you do that one....and so on. This will literally double the amount of extraction mats you receive from bounties.
As for your main question; My first choices were Cindercoat, Unity, and Furnace. A great set of item passives for a HC r6 Monk. Looking for Shenlongs to equip so I can replace the Furnace passive with Flying Dragon.
Zodiac cubed + Focus/Restraint equipped......really great for some builds. It's what I use for my HC r6 Monk when in groups, as Unity isn't a viable option in party play.
Right now, many of the top solo Monks aren't using Furnace to push grifts. I wouldn't either if I had the right gear. The thing is, due to the changes in Grift dynamics, a big part of getting a good time in a Grift is how fast you can clear white (regular) enemies. Furnace will not help you do this, so many people pushing for top placement are finding other options to cube as a weapon passive other than Furnace.
is there less elite/champion groups in grifts now too? The furnace would help with clearing these mobs as well.
Thing is, I'm pushing HC Grifts (currently ranked solo #8) and once you get over tier 50-ish, those white mobs stand you up and waste your time. In 2.2, the elites weren't the problem, it was the RG. There's been paradigm shift now, as less onus has been put on the Grift Guardian's health.
Look at the solo boards. That tells you much. Most of the Monks above me aren't using Furnace as a passive, and there's a reason why. I have no other better option than to cube Furnace, but what's happening to me is I hit a hard wall after clearing a 54 in HC. I simply cannot keep up with the timer at tier 55 because my weapon passive is a Furnace.
For some classes, Furnace will end up being BIS. Barbs, for instance, don't have a lot of good alternatives when you include the cube, as FotVP and Gavel are essentially mutually exclusive as far as high end builds go, and no barb leg weapon really syngerizes with WW.
Monks, on the other hand have quite a few interesting weapons that work well together, making them better than furnace (lions claw, flow, fist of as, etc).
On topic though:
Jewelry: RROG, zodiac, unity, convention
Weapon: furnace (SMK/DoD for WD, a bunch of equally good options for monks, etc)
How does extracting the chance to double attack speed from FD help with spirit generation? Just by substituting another weapon?
Because unless I'm horrifically wrong (and it wouldn't be the first time...) doubling my attack speed would increase the number of strikes I land, as Spirit Generation is on a per hit basis, the more hits I can land in any given time, the better.
But I could be wrong, I've never really looked into the mechanics.