So the empty tower/world problems I was having a while back resolved themselves - though it was pretty much a whole day with no connections to anyone else (Live worked fine otherwise).
Anyway, I'm now in the cave farming phase myself. I've gotten tons of blues and have pretty much maxed out my armor (going from 21 to 24) via that route. After probably 3-4 hours total spent there I finally got my very first ever purple engram. I didn't even see it - it just picked up with everything else (it was probably buried in the horde of ammo). Then I accidentally scrapped a blue engram when I was trying to clear out the green junk. I was in a hurry because others were waiting for me to get out of the cave

.
Much to my relief, though, when I finally got back to the Tower, my purple actually turned into a Legendary. And it was a nice one too: a Pulse rifle. That is what I had been using anyway and it is pretty nice to get your primary weapon upgraded like that. Though I probably would have saved my Exotic purchase (if/when I ever get enough coins) for that. I couldn't imagine finally getting a purple and have it downgrade though. Though it sure as hell took me long enough to get one - seems like I should have had one drop before that.
The thing is, I swear it is doing much less damage than the upgraded level 19 blue that I had before. And that is despite the base damage supposedly being more than the upgraded damage of the other weapon.
Oh well - at least now while I grind, I will also be upgrading that, so that provides a little more "point" to doing it...
I also finally got the "no one dying on a strike" achievement last night. I had done the easy Earth one 2 or 3 times since I've been at level 20+ just because of the "no dying" bounty. But interestingly enough, on each of those runs, one of my level 20+ squadmates somehow died (so I got the bounty but not the achievement). Last night I'm on the second hardest strike (level 22 I think) and 1 guy drops out. So it is me and one other dude and somehow we both avoid dying. I came pretty close a few times for sure.