The solution: yes, ride with the seat "flat" on the saddle and balanced over both seatbones, but also use the balls of your feet with soft knees and shoulders back and down with engaged "armpit" muscles and elbows down to keep you balanced over the saddle and not flopping loosely like so much sand in a bag.
Think of a dot painted on the rider's point of hip right where the breeches pockets might be, moving in a circle during each canter stride: in collected canter the circle moves more in a vertical oval, while in extended canter the circle is more of a horizontal oval.
Important for me is quietly having the rhythm of the transition in my head, and not hurrying the transition. Rather, calmly and quietly establish a good balance with the horse in self carriage and light in the hand, then quietly give the clear aid for the canter trans (for Centerline horses that is to step into the inside stirrup and think of turning the rider's sagital plane slightly to the outside), wait for the horse to respond, then calmly continue the new canter rhythm enforced by your quiet seat (ie ball of foot in stirrup, soft knee, upright position).
Summary of pearls:
- Quietly establish the rhythm, whether that is counting, feeling it as a musical beat, or however, but never rushing rather calmly directing the balance and rhythm with your position. Maintain the rider's correct position asking for balance and lightness even when mistakes occur, and before, during and after all transitions. Test that the horse is balanced and light in the hand at all times.
- Avoid trying to be a "balanced sandbag." Rather use the balls of your feet from the stirrups, soft knees, shoulders back and down with armpit muscles engaged to stay kinetically correct in the canter stride. Use these aids to ask the horse to lift his whithers in collected canter or free his shoulder in extended canter.