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Dynamically and nonuniformly updating object bounds

Static mesh bounds are calculated when the object is imported. And one can edit them by setting the bounds scale. I would like to update them at runtime nonuniformly.
I want to add a material function to all materials present in the world (so this would ideally also apply to skeletal meshes, sprites, etc as well) that can non uniformly transform them via world position offset. The problem is that there object bounds do not update and thus popping would be an unavoidable side effect of this as the transform extents would be in the order of tens of meters. This is to be a visual effect so physics are good and do not need updating.

If needed lets simplify it a little bit for a start and say that that the transform only happens along one arbitrary axis

Demo image of desired effect:

Is there a way around it other than disabling the culling all together?

Is engine source modification mandatory?

Anyone done anything like this, pointers?