Thank you all for your replies and suggestions.
Just to clarify, here is what I have in mind:
View attachment 41206
I'm pretty sure we can't bend the 0.6 x 2 mm strips horizontally, so I thought we could attach them to the binding strips and bend them together.
We have both HHG and fish glue in the drawer, but I do wonder if I can get a satisfactory bend without any moisture at all. I'm not saying we would soak the wood before bending, I've just found that I am more able to get the wood to do what I want it to when I give it a little steam (from a moist rag on the pipe) or water (from a spray bottle) during bending.
I've heard elsewhere that Titebond II or III can be used when you want to bend laminates, but I've never worked with either of them before.