Move object whilst maintaining live bend, without deforming the object


New to Maya - I have created a mobius strip animation which involved deforming my object using a bend and a twist, and then animating the twist to create a spiralling mobius strip animation.

I now want this animated mobius to bob up and down using the move tool, however when I go to keyframe the Y translation, the bend deformer is also effected and deforms my object.

Because the bend deformer is required for the animation, I can’t delete the history to allow me to move the object with no deformation.

I tried to animate the whole object on a motion path, however I get an error saying my object already as an input connection.

Could someone explain how I can animate this?