After probably 25 tries, I finally beat this set dungeon. I ended up using the Pirhanado and Corpse Spiders to trap the elite, and rolled a few items for extra damage to beef up my Firebats (which I thought was overkill, but ended up being crucial). I also included my Wormwood, Haunt, and a Ring of Emptiness.
I personally had no trouble with the Toad of Hugeness challenge, I just used Corpse Spiders to lure my Queen away from minions (so she didnt kill them) while my Toad sat there and licked them like crazy. It's worth noting that if an off-screen elite is hit by a Toad lick, it will apply a DoT, and with a high damage build this can cause an accidental dungeon failure.
Whenever an elite came on screen, I did my best to clear the area and isolate him, and stay a good distance away, to keep the locusts from Wormwood off of him.
Then I hit him with Pirhanado and Corpse Spiders (to lure the queen to him).
Usually within the first two hits from the queen, the elite becomes webbed, and I would rush him, hit him with Haunt, and slam him with the Firebats.
Basically my plan was to one-shot them all as soon as they appeared webbed, and it only worked with insta-kill level damage (1.2M sheet dmg with multiple Firebats items, listed below), no minions around the elite (to make sure the Queen webs directly on the elite), and making sure they had a decent amount of health to begin with, so they could endure the tornado and queen long enough to be webbed.
This still involved a good deal of luck (I failed once because an errant Haunt killed an elite off screen), and timing (the visual cue for being webbed is subtle and I missed it a few times) but it got me through.
I don't think all of the following Firebats items are necessary, but they helped me hit hard just with Firebats, which ended up being the key to one-shotting elites only when I wanted to.
Here are the relevant items from my build, and while not all of them are necessary, these are the ones I thought worth mentioning. Depending on your dmg / toughness ratio, you might want to use Mantle of Channeling, or you might not need it at all.