I concur with your analysis, mostly. Cole adapted to your game. You didn't accomodate equally - leading to a slew of poor BH's, and top-to-top rallies in which you didn't dominate anymore.
About taking initiative, even in the first match I think I saw quite a few rallies in which both you and Cole were hesitant to make the opening move, and though you won it, there were quite a few points in which you not opening up eventually gave Cole the opportunity to kill the inevitable weaker push at some point.
Your footwork looks really good, by the way.