GTs58
I'm the Wiz, and nobody beats me!
Found this picture of a 58 Schwinn Spitfire. (Rear rack has been added.) Thought you might like to see another pretty original bike. Pretty sure the seat is 59 and later.
View attachment 1246165
I think that 58 had this style seat
Two toned, rivets along the side, no Schwinn script S.
View attachment 1246167
1958 Hornet image. And I do believe the OP's 1957 Spitfire had this same seat originally and it's also seen on the 1957 Flying Star catalog image. No two tone mattress type saddle was used on the 57 Spit.