I'm soloing right now, just doing the first missions in The Dust. I'm using a Bee (had been swapping it out for an Impaler but I can't really be bothered any more), a slagged Conference Call, Unkempt Harold, Hawk Eye and Cobra with my Zer0 who I respecced for sniping. I'm still level 51 (about to hit 52) and I can kill level 53 Scavengers with the CC until they're slagged and then 2-4 Harold shots, as long as the distance is just right so that I can actually hit them (I suck at leading targets) and hit them with a lot of the projectiles. Huge damage, awesome gun, but best of all it's quite easy to get in the Torgue vending machines.
And yeah, my Bee has 17448 capacity, which is absolutely dire for actual combat. I do snipe from a distance but in this mission (Too Close For Missiles), I'm forced to get up close. Like I said, I can't be bothered to switch to a decent shield, so I can't really complain that I keep dying now. At least I can take down a Goliath in FFYL now though (provided I slagged him before I went down).
Edit: Ended up getting to level 53 tonight, I was going to solo my way through the dam but thought better of it. Joined a random game, had to re-do the Dust quests again (really quick the second time though) then we went through the dam, went back to Sanctuary then went back to the dam to do the other two quests there. There were plenty of deaths but it wasn't too hard, really. I'm still mainly using my level 50 legendaries too, I'm too attached to them to go back to greens and blues... Might have to crack open the Sanctuary chest soon but I think I might leave it until the Preserve as I'll need all sorts of elements to get through that.
Does anyone know if it's possible to farm the Doctor's Orders boxes for legendary loot midgets? If not I guess I'll find out tomorrow night maybe.