Sugar, can I go into a jealous rant?
You are sooooo lucky to have a T who recognizes your individual needs and works with them! If my T did one of those things...understood why I like emails, accepted to receive one in the way you described, left it open for more support when needed, showed concern/caring/sincerity to help me, or most of all, checked in with me on how I'm feeling about things, I would celebrate!
I think you have a winner
And definitely, you have company in not processing/internalizing things until AFTER session.