Like most things Hunter Arms, it's complicated.
The Wadsworth patent FE was introduced with the Double Barrel Trap in 1920
The early FEs were long and short & blocky
The Schnable was introduced in 1922
At some point the reinforcing rod was not visible at the end of the FE being within slot in the FE
A more attractive Schnable BTFE was also available, but I don't know when it was introduced
and "Skeet Style" introduced in 1929
There were several "Skeet Style" that did not have the reinforcing rod
BTW the Smith SBT BTFE did not get the reinforcing rod until about 1931
Threaded Mode