The steel plate seems to have been introduced when they adopted a five-draw qualification round to determine which 16 contestants would advance to the man-on-man shootoff. I think this went hand in hand with the development of the J-Ladder.
In 1996, Olympic Champion shooter and Marine Major Bill McMillan entered the Leatherslap and ended up 17th in the qualifying round, thus missing the shootoff for the trophies and money. Cooper noted that “[t]his serves to point out the pre-eminence of Big Bear Lake as the modern center of combat pistol competition. No matter how good a man may be elsewhere, how he measures up here is what counts.”
The first year things were not that sophisticated. So no steel plates yet.