I believe in the science of killing surface bacteria in this example of using heat when barbecuing. But in your case, the meat stayed in the higher multiplication temperature zones long enough that you had a higher population of baddies than I feel comfortable with eliminating. Granted, the baddies will become less active as the surface temp rises past 120°, and they will die as the surface temp rises above 140°.
My standard drill on long cooks, especially overnight cooks is to make sure the pit is running well enough for me to walk away for a while, or catch a few ZZZZ's. And that first 2-hours is really important to me, so I would toss it.