You hit on a lot of interesting points. I was always under the impression that the idea of the heavily armored lancer first appeared in western Europe due to Sarmatian auxiliaries in the Late Roman Army. Maybe I am mistaken but it seems like a plausible impetus for the expansion of the role of cavalry in western Europe during the Dark Ages.
Regarding Spain, Al-Andalus definitely played a very important role in shaping Medieval and eventually, Renaissance society.