Thanks for the reply, Tom, I do appreciate it.
The crazy thing is that Foster Reynolds actually used yet a third wrap design on the "Regent" cornet that he produced under the Ohio Band Instrument label. That was at the same time he was making the original F.A. Reynolds horns. The Ohio Band design has a short amount tubing leading straight into the third valve, then a "S" design coming out of the first valve and into the bell.
Pics here.