Autopsy timeline - Where in the world were the morticians?

[Micah Mileto]

William Manchester's 1967 book The Death of a President  (based on interviews with Joe Gawler, Joe Hagan, Dr. Burkley, others) and Jim Bishop's book The Day Kennedy Was Shot (based on interviews at least a couple of Gawler's employees) have statements indicating that the morticians from Gawler's funeral home arrived at the autopsy late. This makes sense considering the Sibert and O'Neil report which implies this. Sibert and O'Neill have subsequently made no statement indicating the Gawler's funeral crew arrived any earlier than the end of the autopsy. 

However, later interviews with Tom Robinson, Joe Hagan, and Joseph Van Hoesen have all had them arriving at the autopsy during the very beginning and witnessing the head examination.  Has this contradiction already been explained?  Without some clarification on this matter, I don't see how anybody can say we know the autopsy ended at 11:00-11:30 AM. With all of the contemporaneous documents out there, I can't find one that precisely gives the time where the autopsy ended and the reconstruction began. 

At first, Manchester and Bishop's book gave narratives suggesting that morticians including Joe Hagan only arrived when the replacement Mahogany casket arrived, and the Gawler's "first call sheet" says the casket was delivered near the end of all post-mortem procedures at 2 AM. But then Joe Hagan gave an interview for Livingstone's High Treason 2 clarifying that the casket was delivered much later than they came into the autopsy. The timeline seems to be up in the air. 

Edited December 20, 2017 by Micah Mileto