a) that I didn't suck so bad at Titan skating

and

b) that I could move as quickly as I do in Titanfall 2, where I've just started to get the hang of Pilot-skating :D

Exact same strat as you posted, except when the Oversoul first pops, nobody shoots it right away. By the time the Oversoul has fully formed, Crota is once again standing and ready to take damage. We would all focus on Crota, make sure he was down again. Then, as when our sword-carrier is well into his 2nd attack on the big guy, I'd use my Nighthawk golden gun and a few sniper rounds to bring down the Oversoul. If you time it all correctly, the music will be done, the sword will de-spawn, and Crota won't have time to summon the Oversoul a 2nd time.

The crew I ran with 2 nights ago (that you helped out with at the end) were just fine waiting to take out the oversoul with snipers until the 2nd downing of Crota.

For the first run, we used the hunters to one-shot Crota just before the sword-runner got to him. The other fire team members dealt with the Boomers, Wizard and Oversoul.

The second and third run, we used the hunters to one-shot the Oversoul. The other fire team members used rockets to drop Crota as the runner moved from the ledge (and dealt with the Boomers, Wizard and any lingering Oversoul).

We used Titan Bubbles mostly for orb generation (Crest of Alpha Lupi helps), but the Blessing of light safety net was nice. In all three runs we stayed at the top of the left stairs until after the second pair of Sword attacks on Crota, when we moved into the left side Ogre spawn room to deal with the Ogres. Stay in that room until Crota passes by on the bridge!

We used the 4 yellow-bar knights at the start to generate up to 12 orbs at the spawn - we kept our Golden Guns fed. Those orbs are also very helpful to anyone with an "Infusion" helmet that can convert them to health.

After clearing the beginning, our first sword-runner ran out and grabbed the chalice, then killed the Sword-Bearer (with assistance from the rest of the fireteam). He moved directly into position on the left side, and didn't return the chalice to the team until after Crota had been downed twice.

Note that the first two sword-runners must combine for 11 RT slams on Crota. Count them and communicate so there's no accidental enrage. The first six slams should put his health bar directly below the "S" in "Son of Oryx". If you get 6 at the start, the second and third sword-runners will need to do 5 each. We kept our best sword runner for the third run.

Keep a person in each tower to deal with the three Knights that spawn there, have someone else with a super ready for the Ogres, and someone with a rocket launcher for the Wizard and Shrieker.

2 Golden Guns and 2 Blessing Bubbles:

Pop bubble to block boomer shots, only kill 1 boomer on whatever side your team is standing (Leaves everyone free to shoot).

First sword runner goes up, gets 3 hits and gets out. Oversoul pops up, Golden Gun #1 solos it while everyone drops Crota again. Sword runner gets 3 more hits...EVERYONE shoots 2nd Oversoul. Return to safe room.

Repeat with a new runner. Just make sure that between first and second sword runner that you only hit Crota 11 times. 12th RT/R2 hit will enrage him. This time 2nd titan pops bubble, 2nd Golden Gunsolos Oversoul. After 2nd set of hits everyone goes to bottom tower to deal with ogres after clearing the Oversoul.

Kill ogres and wait for Crota to move, don't go back to safe room it will save you time. Instead everyone up the stairs, pop bubble while runner gets swordbearer. 6 more hits and he's dead.

This takes a couple tries to get the feel for it, but we found a way to reliably pull the oversoul only once per attack on Crota. The trick is to destroy the oversoul as late as possible. I was running Golden Gun with Celestial Nighthawk, which made this a bit easier:

Exact same strat as you posted, except when the Oversoul first pops, nobody shoots it right away. By the time the Oversoul has fully formed, Crota is once again standing and ready to take damage. We would all focus on Crota, make sure he was down again. Then, as when our sword-carrier is well into his 2nd attack on the big guy, I'd use my Nighthawk golden gun and a few sniper rounds to bring down the Oversoul. If you time it all correctly, the music will be done, the sword will de-spawn, and Crota won't have time to summon the Oversoul a 2nd time.

Pop bubble to block boomer shots, only kill 1 boomer on whatever side your team is standing (Leaves everyone free to shoot).

First sword runner goes up, gets 3 hits and gets out. Oversoul pops up, Golden Gun #1 solos it while everyone drops Crota again. Sword runner gets 3 more hits...EVERYONE shoots 2nd Oversoul. Return to safe room.

Repeat with a new runner. Just make sure that between first and second sword runner that you only hit Crota 11 times. 12th RT/R2 hit will enrage him. This time 2nd titan pops bubble, 2nd Golden Gunsolos Oversoul. After 2nd set of hits everyone goes to bottom tower to deal with ogres after clearing the Oversoul.

Kill ogres and wait for Crota to move, don't go back to safe room it will save you time. Instead everyone up the stairs, pop bubble while runner gets swordbearer. 6 more hits and he's dead.

At first, some were expecting people to just know when to shoot. We quickly stated that the sword guy had to say something (I have the sword...then say something when ready, bring him down, shoot, etc). So it was the swords guy choice. I then called 3,2,1, shoot for the second rockets. I called my 1 attempt (I was 3rd so it was a kill) when I hit the rock left that you wait on. Then immediately went towards him. Unsure of Zero or Chicken's placement. Certainly could have done it a bit earlier but I went with being sure I was ready.

I called it when I was on the ledge. Jumping up and using the sword-swing to close the distance allows you to be in position as Crota is going down. It wasn't really an issue to get 3 slams in per down.

I called it slightly too late the first time I jumped up because I'm used to a different crew with different timings. In retrospect, it probably would have been wiser to have the most experienced sword runner take the caboose and finish him off. That way, you get any screw-ups out of the way before you're too invested into the fight.

That being said, the Crota fight felt much easier than the Ir Yut fight.

Left Knights, Adds, Wizard, Shrieker
Left Tower
Middle then Left Adds, Wizard, Shrieker
Middle then Right Adds, Wizard, Shrieker
Right Tower
Right Knights, Adds, Wizard, Shrieker

We also had the Right team tasked to assault through to Deathsinger and kill the knights that spawn in her room after the shriekers go down, while the Left team raced back to middle to kill the adds closer to their spawn after she shrieks in fear.

it really didn't seem so complicated in practice once folks just razelightered everything.

There are probably a few seconds to be saved at the shriekers by blocking their death blasts with a titan bubble. We used my Sunsinger as a human shield instead

It did seem a bit shorter, but we got it done in 3 sword users. We also seemed to have 4 people who felt comfortable with swords.

We did the same, but having 4 ready to sword is probably how teams should prepare. Reddit describes 16 slams to kill (at 400 light), and he enrages at 12 or 13. Anyone should be able to get 4 hits (two per down), but if you can get 5 and 6 you can do it in 3 runners.

So that was only our problem when people were using Fusion Rifles to start...

Hey, if it's going to give me a 400 Light of the Abyss, I'm going to use a 400 Light of the Abyss.

Thanks, Chris! So you ignored the first Oversoul (triggered after downing Crota once) and only dealt with it after downing him the second time?

Correct, it seems to NOT trigger a second one then. I heard it actually resets the Oversoul, but can't confirm. Either way, with Snipers it was easy to take it out, 2 or 3 from each after the last rocket. So that was only our problem when people were using Fusion Rifles to start...

How tightly did you manage the Boomer and Wizard kills? Our failures were usually due to the their interference at the wrong time - were you dropping them consistently just as the Sword runner was getting into position?

Not as tight as we should have. We did get a Wizard in the way of rockets 1 or 2 times, but we just sent a second (even though it may not have been needed). We could of 100% done this better, we basically just called them out and killed them (my shot was terrible so I would constantly miss my first sniper shot), but it really didn't take away from much since the Chalice was there.

The sword timing seems much narrower in this variant - 3 hits not guaranteed. I'm curious about the timing you used for the rockets - do you remember where your sword runners were when they called for the rocket volley?

At first, some were expecting people to just know when to shoot. We quickly stated that the sword guy had to say something (I have the sword...then say something when ready, bring him down, shoot, etc). So it was the swords guy choice. I then called 3,2,1, shoot for the second rockets. I called my 1 attempt (I was 3rd so it was a kill) when I hit the rock left that you wait on. Then immediately went towards him. Unsure of Zero or Chicken's placement. Certainly could have done it a bit earlier but I went with being sure I was ready.

It did seem a bit shorter, but we got it done in 3 sword users. We also seemed to have 4 people who felt comfortable with swords.