How can a shield winding in the transformer be helpful without fully covering the core?
The shield does not assist against EMI - its protects against ESI - although the two are liable to walk hand in glove in this case.

ie the shield is an electrostatic shield and reduces capacitive coupling
 and not an electromagnetic shield which would reduce magnetic coupling.
 Needless to say, an electromagnetic field would be a bad thing [tm] for the interior of a transformer. 

The shield is effective wherever it places a grounded capacitively coupled sheet between any primary and secondary parts that would otherwise be capacitively coupled. Even imperfect couplig reduction is useful 

Electrostatic shields - Canada transformers



Single layer winding as an electrostatic shield

EE times - useful

Useful images