Whereas the "iron on" interfacing might give you structure, you have to think is it the correct structure. I know this isn't twill but you are making stays. When I make stays I have 4 layers,
1. Outer
2. interfacing
3. interfacing
4. lining
The Outer and both interfacing layers are sewn together with the boning channels. That way the 2 interlining layer create a pocket for the boning. After the stays are boned, I stitch in the lining and the bind them.
Just food for thought.