Question Constraint on local x world space

Hello!

I'm in a situation where I have a snake-like object that has its procedural movement controlled by a set of Damped Transform constraints. This object is parented to a platform, and needs to move with it.
The thing is, I want the snake-like movement to proc when the snake itself moves, and not proc when the snake is moved by the platform.

My current output:

My intended output:

For the sake of this video I just turned off the animator before moving the platform. This is not a viable solution because the snake should be able to move on the platform WHILE the platform moves. Any ideas on how to solve this?

I tred using parent constraints instead of parenting, as well as a bunch of the transform/position IK constraints, with no success. I've only recently started to explore the animation rigging package so if I'm overlooking something obvious, please bare with me.

Thank you.