AFAIK, the only S&W that had the serial stamped on the front strap was the Regulation Police Model, which always came with wood "filler" stocks to make it round butt. Those guns also have a "step" in the backstrap, the only S&W's to have that. Its purpose is, again AFAIK, not known at this time though there has been speculation.
One point that confuses folks. S&W (with the above exception) ALWAYS put the serial number on the butt. But at times, Colt put theirs on and under the crane, where S&W put its assembly numbers.