Quote Originally Posted by Rebellious Waffle
Doesn't immediately pertain to the use of two-handed swords in a cavalry context, but there's a lot of good background about the history, use, construction and utility of such blades.
From the links you posted (Oakeshot XIII page) :

"These swords were devastatingly effective in slashing attacks from horseback or two-handed use when dismounted."

... which suggests these swords were used by mounted warriors, probably with one-handed swings to the side, and normal 2h use when off the horse.
Unfortunately, no other links are provided to support this affirmation, except the original source books.