That kind of origami “theoretically” doesn’t allow flexion in 2 axis, but just in one.
A “twist” or torsion effect is a shape that shouldn’t be achievable by that origami.
(In fact, there are few origami modules that allow many deformations, most of them doesn’t allow “negative” curvature either…)
In the pictures it “work” because the paper is not 100% rigid (like a math model), but somehow “elastic” (very elastic).
Applying an “inside” force to bend/twist your origami would give you non-uniform, unexpected and ugly results.
You should prefer to use a rigid (or semi-rigid) shape/surface/mesh as attractor to gradually put-in-place your origami.
(This is an old video of mine, old grasshopper, old kangaroo)
See at 9:17 and then at 10:20 … (turn off audio
I did use a shape to attract “valley points” (pull to surface) , and another shape (from offset) to attract “mountain points”. By changing the offset you can set the opening/closing of the origami.
And you can add some lashes + anchor point to manually fix your origami in position.
My idea is:
Origami(s) are rigid, theoretically… you can’t use them if you don’t enforce them.
It’s easier to just use a predetermined shape.
This is just an opinion.