I've had amazing luck these past two nights. Started with just running up some spare Greater Rift keys from 35/36 towards tier 40. In one of my tier 36 rifts, the RG dropped this for me:
Considering that this was the only item in the game I hadn't found a GG version of, and this one rolled amazingly well for me, I was ecstatic to finally have such a strong Furnace. My previous 2 were rerolled to reach 3400 and 3550 DPS, and the latter was donated to me by a friend that found three in two days.
Then in the very next tier 36 rift that I did, this dropped:
My amulet before this was a BT Cross with 6xx INT, 99 CD, 9 CC, and OS, so I gained a better CC roll which is critical while using a Furnace, and a little extra CDR placing me at 44.96% with a free roll.
So used these two new items, and switched over to a dull DPS spec, then ran the seven Greater Rift keys I had up to tier 39 last night. Starting again tonight, I carefully went through all seven keys successfully (though by as little as 5 seconds one time) giving myself another seven attempts at finally beating tier 40, which is where I lost interest after failing by a few seconds to Saxtriss a few months ago.
So I started running my tier 40 keys, but with poor luck. Very minimal density with Winged Assassins the first time, then more Winged Assassins with archers on a high density, but long single level for rift 2.
Then on my third try, I got a nice density rift without any severe threats:
I finally cleared tier 40! and still had 4 attempts to do even better. The next rifts was bad. I had three floors that were almost completely empty, but the fourth floor was heavy zombies. Too late though as I lost the rifts by about 15 seconds on the RG. The next rift also didn't go well due to a death on a very long first floor, causing me to kill the RG 5 seconds too slowly. Then this:
I got another successful tier 40 clear! Great density the whole way through, though it got a little messy a few times with dangerous elites, though spawning Stonesinger at the end saved more than enough time.
So after quitting any attempts at solo Greater Rift ranks several months ago, I came back from rank 480 with an average tier 39 clear, and jumped to rank 132 thanks to my Furnace (also after having given up hope of getting a good one before the new patch)
So a few tips to anyone that is struggling to clear a new tier: 1) Keep trying. The randomness to map and monster spawn makes a huge difference the higher the tier gets. 2) Know when to stop kiting forward. Most of my deaths at tier 39 and 40 were from getting too agressive. 3) Be aggressive anyways. You won't make a new personal best by over cautious. 4) Don't waste time trying to clear a bad rift. Once it is obvious you won't finish in time, just leave the game and try again. 5) In some rifts, you may have to skip a floor. A low density rift or Morlus and bugs will kill the run if you try to fight it anyways.
Here is my profile. It has the exact gear and skills I used tonight.
http://us.battle.net/d3/en/profile/Enremeit-1915/hero/32329467
The only change is that Paragon points place me at roughly 600k Life and 12M Toughness.
Good luck to anyone that is still trying to increase their solo rank.
Update:
Officially in the top 100! A clan member got me three 41 keys and four 42 keys. That was the third of 41's, and the other two were also fairly close. The tier 42 attempts went very poorly. I skipped the first two after running into elites that I could neither kill nor skip, and the other three started out strong, but I couldn't spawn RG with enough time remaining. I'll try again tomorrow.