As far as modern cattle-beasts are concerned however, if the
> lactating cows aren't milked every day, the milk does build up and causes
> pretty extreme discomfort and (I've heard) can even kill the cow.

That is true for any mammal that has nursing suddenly cut off. A
friend's baby died, and she had to extract the milk (that was one of
the saddest sights I have personally witnessed) for several days when
her breasts got too full.

 Suckling
> does help, but just that alone tells me that significant milk production
> happens when the udders/nipples are not being directly stimulated.

Milk continues to be produced, and the udders of a cow fill, but milk
is "let down" when the baby suckles. Farmers massage the cow's udder
prior to milking to cause let-down.