I would not tea stain it. It's too unpredictable and totally undoable. The wheat and the sunflower are going on top of the KT section, right? That will definitely tone it down. You might also audition a fairly narrow border of the white TOT inside the barn board print and next to the center section.
I think part of the reason the white looks so stark is that it's only in the center band. By adding a narrow frame of the same fabric, like matboard, you'll mitigate the "look at ME" effect of the white. You could even lap the appliqués onto the white border a bit to include it more. Certainly won't hurt anything to audition it.