Any advice would be appreciated. Also if you go through the text, you'd notice I say it's next to impossible, hinting at it being a difficult challenge and asking for help so others can see this thread, hence the click bait title, and get the help they need as well.

The only advice is to have 3 people create a plan on how you will tackle it. Run it multiple times (with the same people) and improve your strategy per room. Note your times going into and out of the rooms and look to improve upon such each run. Increasing your light level will not help as Nightfalls set themselves to your level (once you're over 240). If the room you're in states, "kill all X opponent" you have to fight in that room. If it does not, you likely can skip that area and just keep pushing through to save time. Some weeks are easier than other. Week 2 and this week are arguably the easiest ones. Week 1 was not as easy, but was still possible. In truth, if your group is struggling on this week's nightfall (no offense) it's because you guys don't have good gear loadouts, gun-skill, teamwork, or a combination of all.