Hi Jodie, there's no way the original customer would order the machine without reverse; it is just that that particular variant of the model 15 did not have reverse, unlike the 15-91.
After watching this video...
http://youtu.be/MrjFNWsajfQ
...it seems clear that the "special order" feature of your machine was in fact the decal combination. As Muv has pointed out, the Indian Star decal on the bed was not intended for the domestic market--your machine was definitely manufactured in Singer's Elizabethport, New Jersey factory, as indicated by the "A-" serial number--so the customer must have specially requested it. After seeing the video linked above, it seems at least one other customer of the era also requested it (unless the guy who made the video is the one who sold you the machine!).
As for which service manual to download, we'll need a little more information to nail down the sub-model. Does the machine have a rotary hook, or an oscillating?