Lorilu, although I am further behind you in schooling, I have found working with the Iberian body type to be such an education! Some things are “easy” with this type, but I have had to really go to school on connection. I like how you described the very small window on neck placement, too. Everything always looks round with my mare, but it isn’t necessarily so!
I’m sure you know this, but the shift from looking connected to being connected can require quite a bit more strength from the horse—and when they’ve been doing the looking connected movement pattern for a while, it can be shocking (and hard) to the horse when you demand true connection.