GT triple triangles are quite stiff IME.

I would imagine the 28's are all that is going to fit through the stays. Perhaps one of the fancy carbon seat posts, cobblr gobblr or some thing that the pros use for Paris Roubaix, and some high end bar tape with well placed gel?

I would also note, I use a set of (much larger) Kenda Kwest tires on my city bike and they are far from supple in feel, in spite of the size.