The easiest way to do it with random people is the one portal method, which is safer. You'll be going through as a group into one portal, then going to the second portal. WIth folks you know, you can get both at once. Both at once is ultimately easier, but it is trickier to get down and has less margin for error.

Take charge, and tell everybody the plan. Send two of your level 30s through the left portal, and have them focus fire on the gatekeeper. Don't kill any other enemies. Just before the gatekeeper dies, one person should head out of the portal to avoid getting the debuff, while the remaining person kills the gatekeeper, grabs the relic, and exits. Behind the portal is a safe place to avoid enemies before you kill the gatekeeper.

While this is happening, the 4 outside should be able to defend the portal.

After the relic holder comes out, minotaurs will start spawning and walking to the conflux. You may want to not put anybody on minotaur duty and just let them go. With an unfamiliar group, an extra defender can be helpful. If you feel like you will be slower, have one person at the top taking them out. Standing behind their spawn I think works best, since that cuts you off from snipers.

Repeat with the right portal. Send through the relic holder since the mark of the void will be applied instantly, and the other player will need a cleanse. Use your relic super on the gatekeeper, which should take him down about halfway, while the other player finishes him off. One the gatekeeper is dead, the relic holder should cleanse the other player, then head out and immediately defend the middle.

Once everybody is outside, the two relic holders should take out the Vex until the portal open, and then focus on one portal each. The stomp attack works very well and you can take out Praetorians all by yourself.

If you push a Praetorian back through the portal, it will respawn right at the conflux and begin sacrificing. This could be advantageous or not depending on your situation, since it won't attack you while it's sacrificing itself.

Sadly I think only the fireteam leader holds the save, but someone correct me if I'm wrong. I'm still definitely willing to help, but I'd suggest starting a new topic to try and get recruits :)

It has to be the same one. So you'd have to beat the gatekeeper part.

Ok cool. So if we can't get a crew together, I can just join someone with a Gatekeeper checkpoint and knock it out?

I have a Hard mode Gorgon checkpoint..