I am not disagreeing with you that the first two parts of the raid are doable at 350ish. We had 3 around that light, and we never felt as if light was what was holding us back. You are correct there.

However everyone I have talked to says that the last section is a different story, and that you want as many 360s as possible.

It's convenient to have as many 360s as possible, but remember that even the last section was three-manned in the first week, and without spoiling anything, you have more than enough wiggle room to accommodate a team with low DPS (the game can give you a free pass if you need it).
"everyone that I talked to". Talk to the three separate teams that I've run the raid with, and they'll no doubt agree that the last boss doesn't cause headaches because of light levels, but because of coordination.

I had to grind to get to 350 even. Tell me how you did it without playing strikes over and over. I'm genuinely curious, since you claim to have spent so much less time than I did getting there and I would love to spend as little time as possible on leveling when the game doesn't make it fun. This is a genuine question for you, so please do let me know.

I was able to get ahold of some high light gear by doing Archon's Forge (Cyber and I ran quite a few with a single group at one point, lots of fun). That's how I got the awesome helmet that I still use, the "But Not Forgotten" sniper (which I got by accident while doing story mission patrol with Sammy the first day), Saladin's Watch fusion Rifle, and high-light class items. Like I've said before, though, I was over 350 before I went to the strike playlist.

After that, I did run strikes, popping three of coins, but they went by quick thanks to Arc burn, and the fact that you're guaranteed two blues at higher Light than what you have up to 365, so as long as you do a few strikes a day, you should have no problem being Raid-ready (note that Sammy didn't really even do that). Still, between that and Crucible, I was 365 in three days before the raid dropped (Cyber was 370, IIRC, and Otter was also raid-ready, and he had school every day that week).
Really, you should be asking Otter how he got raid-ready so quickly, since he played a fraction of what the rest of us played.

Also as far as I know crucible drops are weapons only? And yes, I did gain a fair bit of levels in the crucible and that was much more fun, but for armor you need strikes.

Archon's forge drops different armors and class items (not to mention tons of Engrams). It was a bit hard to play consistently the first week, but the drop rate is great (especially since it's a Public Event, and the offerings have been greatly improved), and if you do Patrol, the Quarantine patrols pay out crazy amounts of rep (and there are lots of them).

I also recommend running Trials. Our very first game, I got a pair of 375 light Gauntlets. As long as you're winning or filling out the bounties (which happens even when you lose), you're getting high loot drops.

I was >340 just by finishing the story missions. The ridiculously high engram drop rate got me the rest of the way to 350, and only then sid I have to "grind" at all. I cant give you hard numbers, but I got to 364 with only a minimal number of Heroic Strikes (10-15 I think? 20 max, spread over 3 days) and I didnt even do the nightfall, play any crucible or edge any factions.

Maybe Im just luckier than you though?