As a late addition to this post, I just discovered this entry in TATHS journal no 2. Hope they don't mind me reproducing it .
"Short (i.e. 7”- 8”) Moulding Planes
Most collectors find these planes occasionally but not in sufficient numbers to elicit great excitement. Nevertheless they appear to be in family of their own and to raise interesting questions. Whence the need for such straight planes, shorter than normal but not down to “thumb size? Why were so many of them made in Scotland and Birmingham many of them have SHOULDER, MOUTH-OPENING OR BOTH ON THE LEFT; (my capitals) possibly the only known planes designed to work left-handed on straight stuff? Let us know about any you have: length, maker's mark, type size of moulding, R or L-handed, side shouldered, bed angle, etc."
Seems such planes are known, although mine is the normal length.