Maybe it's me, but I think someone has misunderstood something here. Are
you sure the method is not referring to inverted spins only?

I have spun almost every aircraft I have flown, glider or powered. I
haven't tried too many recoveries with the stick back. All the 1-26's I
have flown would respond to opposite rudder even with the stick full
back. However, unless the stick is moved forward soon after rotation
stops, you might find yourself immediately in a spin again.

Both my 301 Libelles required some stick forward to regain rudder
effectiveness.

The document I'm referring to was written for test pilots, and I'm
reading between the lines that it's understood the stick would not be
held back once the rotation stopped. In fact, the method cited
suggests letting go of the stick, rather than holding it back.

There's more detail in that document, to the effect that if the stick
is moved forward while the aircraft is still rotating, it can
accelerate the spin and make matters worse. Also, on most power
aircraft the elevator blankets the rudder when held down: not an issue
for modern sailplanes.

Take a look at the reference yourself: it's a PDF, and the section on
spins starts on page 24.

What struck you is what struck me: no reference to moving the stick
forward at all, and if you let go, then as long as the aircraft is
spinning the stick will actually float back.