Went through there yesterday and use the D1 entrance. The private TSA is still nice, and Delta staff were extremely friendly. SC was quiet when I got there in the evening and only picked up slightly as it got a couple hours later.
One thing I did notice in the current D1 'waiting' area... they have much better comp beverages than the SC (Silver Oak cab, Tattinger champagne), and even offered a couple light appetizer 'amuse bouche' type items.
Still the location is a crappy spot on the arrivals level, and you're better off going to the level 2 departures and taking an escalator down to baggage claim to get to the D1 entrance rather than waiting in the LAX traffic mess headed to the arrivals area. Basically no change to that situation since I was there last year.