As a previous post suggested, the Trek's set up indicates the frame's too small based on seatpost extension, but the Technomic stem is a short one, you'd expect it to be 100-120mm long.
I'm about 5'10" 30" inseam, and ride anything from 54cm c-t to 58cm c-c seat tube. 55cm is my supposed ideal. But my 57cm frame is the most comfortable.
I surmise you are the opposite of me, longer legs, shorter torso. (which makes you harder to fit)
If the Gazelle measures 56x54, I think you're fine. And she is a beauty!