My understanding of the origin of "Long Colt" is a bit different than your own - that when the .45 Schofield was proposed as a serious competitor to the .45 Colt for use by the Army, and was (officially or otherwise) adopted by some units, "long" was added to minimize confusion since the Schofield cartridges, being shorter, can be fired in Single Action Armys, but .45 Colts are too long for the Schofield cylinders.
The problem with that is that the .45 Schofield was commonly called one of several things, but it was never called the .45 Colt or .45 Short Colt. It doesn't make sense that anyone would have to come up with a way to avoid confusing two cartridges with different names.
Elmer Keith (and other sources) explain that in addition to the .45 Colt and the .45 Schofield, there was a third round, distinct from either of the other two. It was headstamped .45 Colt and apparently sold in boxes with similar markings.
It makes a LOT of sense that that people would distinguish between the two identically marked rounds by asking for the long one or the short one.
The link below contains more information.