I actually like your idea of address. You could do it 'Dear Secretary-name / Old-T name ?' I think that is just a request for clarification and is totally in your rights. I WOULDN'T pretend you haven't noticed anything because you are denying yourself something you are entitled to - that is - knowing WHO you are corresponding with. And having the other person know that you know.

My sense is that she didn't tell you it was her that was communicating simply in order to avoid complicating the situation. It would have been more ethical for her to have just clarified with a brief note, but lots of people try take shortcuts.