For touring with the Brompton, I use a Kelty Redwing backpack that I hang off the back of my seat and strap down to the rack. I stole this idea from Russ and Laura and their blog, where they show how to do this. Russ used a piece of dowel that he strapped to the saddle's attachment holes with pedal clip toe straps.
I tried this technique.
In this first way, I hooked both the adjustment straps and the backpack straps over the dowel. The straps fit very tightly, yet still didn't stabilize the backpack as well as I wanted.
Next, I only slipped the adjustment straps over the dowel. this worked a little better, but I found that the dowel would tend to slip toward one side or the other and the back pack would start to hang more to one side instead of being centered on the back of the bicycle. And also, the dowel was kind of long and stuck out pretty far from the seat.
After getting back from the Syracuse to Buffalo trip, I thought I would try a similar approach with a different material.
I went to the hardware store and bought some 3/4 inch schedule 40 poly pipe and some elbow and tees. My idea was to cut and assemble them as shown.
I thought that the tees would allow me to use the toe straps to hold the assembly more firmly, so it wouldn't slip from side to side. By rotating the elbows, I could make sure that the adjustment straps on the backpack straps would not slide around.
I dry fit the parts and tried it. I liked how the tees made it possible to strap the pipe to the back of the seat in a way that would not slip, but I realized that the elbows on the ends were overkill. The backpack straps never even got close to the hooks when cinched down tightly. I removed them.
And I was left with only this, which is enough. Maybe the small pieces of pipe on each end aren't even necessary.
Here's a good view that shows the adjustment straps hooked over the pipe and the sternum strap wrapped around the carry straps to hold the back pack in place. This solution has been firm and it holds the backpack evenly in the middle of the bicycle.
I like to use a back pack and my Touring bag, because it makes it easy to carry the gear when I'm walking through a bus or train station. Backpack on the back, T bag in one hand, and bicycle in the other.