I once had a fluttering noise that I spent some money on trying to solve. It turns-out it was the fan shroud. The engine will move around on acceleration and a slightly out of adjustment fan shroud will cause a fluttering sound.

I realize the thread has focused on involved solutions to the problem and it may indeed be an involved problem. However, my experience dictates that mechanics miss these kinds of simple answers. If it were me, I'd move the fan shroud a bit (check adjustment) and see if it changes. I'd check my viscous fan clutch, bolts, etc at the same time.