It would probably be useful to look at how other people have solved a similar problem, too. Are there any examples of people creating similar deformations in Maya? Do they have custom deformers for it? There's a good chance they used some combination of existing Maya nodes, at least for part of the solution.
From my interpretation of what you've described, I think it might be worth putting some sort of lattice deformer on your structure, then scripting the motion of the control points on the lattice. You could simply step through time and key each point on each frame. Once you have that working, you could look into more elegant ways to do it.