Personally no I don't. But I don't care about my head/chest position as much as my low back position and the loading of the hams/glutes. As long as those elements are tuned, .....well it's a good morning. Your chest is supposed to drop. That's what makes it a "chaos training" tool, or a weak point tool.
Of course I try to maintain extreme tightness and keep the chest up, but in near maximal efforts that just isn't going to happen.
Storm, did you notice any carryover from seated good mornings? They seem to be a love/hate controversy for a lot of people due to the biomechanics involved.