Is there a way to bake deformer graph animations in level sequencer into an animation sequence

The fact that the duplicated asset with constants works for you is a good sign.

Forget about the control rig for now, if you just add a single variable to the deformer graph like this, do you see similar deformation? Note that currently every time you change the variable value in the deformer graph editor you will need to hit compile again as live update hasn’t been implemented for variables.