How close together are the serial numbers? I would assume the .44M is earlier than the M27, but since there is no distinction in serial order for different models, it might give some insight as to how narrow the window is for 4-screw, non-model stamped. Then there's the possibility that maybe the orders to model mark and screw deletions filtered down to the respective models a bit differently, given the .357M/M27 has a unique frame within the N frame guns (top strap checkering), or was that done as soon as it was determined which model the frame was going to get used for?
Wouldn't it have been grand to have been a fly on the wall at S&W during this period, and then later be reincarnated as a S&W collector?