Panic, the stock gears are held in place by a solid steel pin. The gear on the 55 and up distributor is cast. I just broke a gear driving the pin out during a rebuild and I was not really hammering on it all that much. Was a bummer, the gear was in usable shape. The nos GM replacement gears generally have a new solid pin but you really do need the right equipment to peen the pin correctly. In the early GM parts catalog (mine is through 59), the pin is specified as a solid pin. The same GM part number now gets you a roll pin. The GM replacement roll pin is the same length as the solid pin, but since you don't necessarily peen the pin over, it ends up a little long sticking out on either side of the gear when its installed. I generally have used Ford roll pins which are shorter. You can safety wire the pin or counter sink the gear just a little and peen the pin a bit. I have seen it done both ways, and I do it both ways, depending on the application, when I am rebuilding a distributor for these motors.
I have never had an oil pump on one of these early 6 motors actually seize but that certainly could be the cause of the issue. I will be curious to hear if the pump was the cause.