Good points. I'll offer my opinions:
1) "- the partial sole must have survived even though the uppers (if it came from a shoe) or sandal straps did not."
IF the sole was abandoned only months before, then a thick layer of leather (or rubber?) might survive to be examined. Also, sole leather may be made of leather tanned by different methods than uppers, possibly making them less palatable to crabs and other fauna. An obvious test would be to leave a variety of foot-wear for the crabs to nibble on, and see what they like and don't.
2)"- the partial sole must give the impression that it may have come from a sandal."
If the sole were thick but completely missing uppers, then Gallagher might have guessed that it might have originally been a form of sandal. I would not rule out the presence of a row of stitching around the edges as being indicative of sandal construction. Crabs might have eaten the soft top layer, leaving the tough (differently tanned) bottom layer.
3) "- the partial sole must give the impression of being "stoutish.""
Aside from assuming that the simple presence of a leather sole after some unknown number of months of exposure might have given the impression of "stoutness", perhaps the thickness or stiffness of the sole remnants gave the impression of being "stouter" than light walking shoes or dress shoes. Note - would exposure to Niku's environment have caused a soft leather sole to transform into a "stout" form?
4) "- the partial sole must be obviously and convincingly from a woman's shoe or sandal."
Here I prefer to defer to "British" knowledge of the time - from my 21st century American background, a "woman's shoe or sandal" would be narrower than a man's, have a more pointed toe, have a narrowed instep, and a more raised heel. It also might me more likely to be made of multipe layers, with fine colored leather on the outside, and fine-textured leather on the inside. The current construction methods of women's shoes in the US are also commonly found in expensive Italian men's shoes, raising the idea that a fancy Italian shoe sole found on an island might be assumed to have belonged to an American woman. However, to follow that idea up, how would a fancy Italian shoe end up on Gardner Island around 1940? My mind boggles!