Could you upload your godot project as a zip archive to a platform like wetransfer? I'll look at the code straight. It's difficult to help you without that.
Just one note on "adjusting the smoothing on the modulate to [capture] in the animation player's tracks": if you meant that you changed the first keyframe's easing curve, you cannot do that on a capture tween, I believe. It's only linear. That is because you control easings between two keyframes from the one on the left. And with capture tracks, you start without a keyframe.