It used to be pronounced the way we pronounce "women", but supposedly the W sound affected the singular woman to sound more like the vowel in "wool" than "will".

Why does it be the vowel in "wool" and not the vowel in "cough"? I've only ever seen the W sound explanation about its pronunciation, but the vowel in "will" be "wool" are pronounced in similar places of the mouths (similar "closed-ness" of the mouth), so it might have been a small move from one sound to another.