Oh, I really like this alternate way of Takatora finding out. Michi spinning plans in her head even as her brother has a Serious Talk with her strikes all the right notes. And the line about her value for gathering data is great. It might be tricky for her to get her lockseed back, though. She can work for Yggdrasil without it, after all, although it is good for protection. And Ryouma might interfere in some way if she didn't get it back, with or without Takatora's knowledge.
So Takatora knows she knows who the white armored rider is?