Need help rolling/coiling a plane on a path

[e.turcotte]

Hello, Im trying to roll/coil something. I know how to do that on a flat surface but im having problems doint it on anything else. I have attached an image of what the mesh looks like, I need it to roll on itself. What ive done until now: I have used a flat curve that I rolled with a bend deformer, then instanced the curve and made a soft geometry. That way I can give the plane the shape I want and keep the roll with the bend. I then used the animation snapshot, and made a blendshape so I dont need to use the bend gizmo anymore. I then duplicate the curve and use the wire modifier to get my mesh the shape I want ( the shape on the side where it goes up and down). That where im stuck, the rolling animation is deformed (probably because the vertex point on the wire curve are not spaced evenly anymore). I tried rebuilding the curves, adjusting the wire options..nothing works. I dont know if anyone has an idea on how to achieve that rolling animation that goes up and down. I cant find anything online. Thanks for any input