[SoCal LS-L]

I would say test the fuel pressure while its going, see what your reading is vs. spec. A very lean engine can idle but cannot produce enough torque to move the wheels, ala stalling out in gear. The seeming to do it while its hot thing also points to the fuel pump, they tend to fail when they get too hot, and slowly failing ones also act worse when they warm up. What does the exhaust smell like when it runs and bogs?