The ASE type serial numbers were bugging me as I knew I had seen them before. Had a flash of memory and sure enough, in "without Warning" the ASC and ASE serials are explained as "ASC being for scout rifles, "ASE" being for section rifles. (pages 57 and 58).
Both these rifles are on the list of known examples given in the book: ASE40-3 had a 3-1/2 power Gimbell scope while ASE40-8 had a 5 power Gimbell scope. Both had mounts described as "Long Base Fired".
Whew, now I will be able to sleep tonight without those serial numbers nagging me. I knew I had seen them somewhere.