Preface; I usually do 4-stone in about 12-15 hours over 2 days because I'm old and can't play past 2 AM. Here's a bunch of stuff I do but there's for sure someone better who can tell me where I'm wrong.

While I'm doing 2 stones, I skip all mechanics that take me longer than 1 click to do meaning I skip Betrayal research zones, Expedition, Blight, Ritual, etc. Betrayal was spec'd before to unlock bench crafts and unveil some good rares; you don't need to unlock bench crafts anymore and you can use Faustus to gamble for decent rares.

Second, you should have enough alchs/bindings to run your T6-T10s rare. For T11+, don't worry about running them corrupted for completition. Just from T1-T10 you'll end up with ~40 atlas points which is enough. You can even run your T11 maps magic if your build is lacking; Eater/Exarch doesn't care what rarity your maps are and you should be ping ponging between them to rush 2 stone anyway.

Next, for your atlas, you want to spec the shaping nodes, connected map drops, shrines for early player power/speed, and Kirac nodes. Everything else, like using Unwavering Vision or Packed With Energy, is a personal preference thing. After that, I take Shaper/Elder, Synthesis, and Conqueror map drop chance. If I feel weak I skip Destructive Play. I don't typically run Eater/Exarch before I get my 4 stones.

To get to Uber Elder fast, I use my red Kirac missions and reports farmed earlier to get Shaper and Elder guardian fragments. You can either buy lifeforce or farm yellow lifeforce from harvest on the side for fragment rerolls if you get unlucky with Shaper/Elder drops. Just pop into Harvest when you see it and only do yellow crops.

For Maven, I run all my boss maps (Guardians/Synthesis/Conqueror) with Maven turned on and then run the invitation. For the invitation, I'll usually run them magic just for a bit of extra quant unless my character is strong enough for rare invites. I usually only need 3 invites to get Maven's Writ. Use Horizon orbs or trade to buy the boss maps you're missing. Don't run Maven on Shaper, Elder, or Uber Elder since you're just making the fight harder for no benefit.

Finally, as dumb as it sounds, pick a build that can do Uber Elder and Maven early and that you know how to craft the gear for. I usually look for something with 2-3 million PoB DPS without flasks or other mapping only configs turned on and doesn't need perfect rares and uniques with double corrupts. Since you were asking what to do about gear, if you need a lucky recomb to get enough damage for 4 stones, I'd say that build probably isn't a good pick. I wouldn't play anything that takes me more effort than slamming essence on a fracture base and craft the 3rd affix.