Having everyone run in circles seems to me like too many moving pieces, which is why we didn't end up doing that strategy. But I guess I can see the utility of it if some group members are not used to raiding and hitting their marks by themselves.

Raid spoilers below

This approach to the Gauntlet can be tough for some guardians due to the number of tasks everyone must perform correctly. Each person who isn't running must get on their platform, monitor the wall to their left (shooting lower when called), shoot their wall (upper when called), melee their psion, and then get back on their platform in time to repeat it - all with good timing. It works, but that's a lot to ask of some guardians.

No, if you shoot lower on yours, you shoot lower on your teammate's too. If jumping off your platform to melee a Psion before jumping back on is too complicated for some people, I really don't know what to tell you. If you watch the video, it's super straightforward.

An alternative approach:
Split the group into two teams of three. Instead of each "inside" person being responsible for a fixed platform and two walls, assign two people instead to follow each runner around the room. With this approach, one of the inside pair ignores the psion - they just need to hop on the next platform and shoot the upper wall. The second of the inside pair ignores the platform - they just need to melee the psion and shoot the next lower wall. The pair move clockwise around the room with their runner. The individual workload inside is reduced, and groups I've run with have all had more success with this strategy.

This is exactly the strategy that I was referring to when I said that there was a complicated strategy floating around. Sure, your personal role is more defined, but it's wholly unnecessary. However, if people want to keep their individual contribution simple, I can see the appeal. I feel like there's a higher chance of screwing up with this method, though.
The video that I included is from our second time ever doing the raid. Last night, once we worked out some connection-based issues (sorry Destroyo!) it all ran smooth as silk for everyone. Zumphry is definitely familiar with your strategy, though, but quickly adapted, so either/or works.

When it comes time for the entire fireteam to run the gauntlet, it's also easier to split up who gets which psionic energy ball - the two teams of 3 just alternate. The "beast team" (that start on beast initially) grabs can energy at the first and third walls, and the "cup team" can grabs energy at the second and fourth walls. It's easier for just three people to call dibs on one of 4 balls (and there's always a spare if there's a conflict).

Technically, that's kind of what we were doing, but spacing it out into groups of two to avoid clutter and/or confusion as to who grabs which energy boost. With our method, the two weakest platformers can take as long as they want, and they won't ever have a conflict with other players, which are far ahead.

The number of balls at the end seems to correlate with how many times you mess up during the initial three stages. There's normally just three balls, but if you screw up once, four appear. And so on... I bet for Prestige, you'll have to slam all six, so it's better to get everyone through now.

Sherpa notes: Obviously the guardians who are best at mobility can run the Gauntlet, but I'd put your best shooters on psion melee duty, the weakest guardians on platform duty, and the guys left over should run.

The past couple of nights, Kupkake and I had to teach a couple of groups our strats, and even though some were blind, everything was easier than when our "pro" group did it last tuesday (we even got 80+ stacks on Pleasure Gardens with a team that had four blind folks). I guess it really just depends on the people doing it. I hear you're a good sherpa, so whatever works for your team. :)