I had a similar problem with one of my LS's, and this is what I did to resolve it; this may or may not help . ... After trying the same things that you did, I took my EGR valves off and cleaned out the passage way's, next I cleaned my throttle body intake, lastly; I cleaned my intake and valves with a bottle of Sea Foam . (Here's how you do that) : look at your intake, in the front you will see two hose's, one big and one small; the big one feed's vacum to your power steering pump . Disconnect that line and get you another piece of hose about two(2) foot long that fits that vacum port . Next start the car and let it idle, then insert the hose that you connected to the vacum port on the intake into the can of Sea Foam . The vacum of the idling engine will suck the Sea Foam out of the can and into the engine . If the engine tries to stall, give it some gas . Let the engine suck about half of the can of Sea Foam, and then let car idle around 1500 rpm's until all the white and or black smoke stop's coming out of the exhaust .
The process that I just described, cleans the intake and valves of deposits that build up over the years . I use this process on the vehicles that I service when there is a lope or misfire that isn't attributed to a vacum leak or tune up . I have had to do the procedure twice on vehicles that had alot of build up .
I hope that this helps you .