Now that I look more closely, I realize that most of the numbers are cast rather than stamped, and so they couldn't be changed for each individual motor. Two of the numbers are stamped, but may or may not have any relevance to my serial number.
Hi. I have an old Scott Atwater that has no data plate. It's a Bail-a-Matic, which places it in the mid-50's. The decal on the hood claims "10 HP" but I believe the 7.5 hp and possibly the 16 hp all shared the same hood, so it could have been swapped, so that's not definitive. The serial number format of these motors is 4 digits, a dash, then 4 more digits. There are a few different such numbers stamped on several different parts of the motor; they follow that xxxx-xxxx format, but they're all slightly different numbers. Some start with "33" which indicates 7.5 hp, and some start with "38," the nomenclature for 10 hp. Some of these are on removable components (such as the housing of the recoil starter) that could easily have been replaced. The number that I would consider to be most authoritative is one that is stamped on the starboard side of the crankcase -- I THINK that's the serial number of my motor, but I'm trying to confirm that it is.
So I'm hoping that someone who has a Scott Atwater could check something for me: Does your motor have a number on its crankcase that agrees with the serial number on the data plate?