MoveAnimatedCharacterMenuItem.cs

using System.Linq;
using UnityEditor;
using UnityEditor.Timeline;
using UnityEditor.Timeline.Actions;
using UnityEngine;
using UnityEngine.Timeline;


// Adding a new menu item to the move/rotate etc commands would be cooler!
// https://github.com/Unity-Technologies/UnityCsReference/blob/master/Editor/Mono/GUI/Tools/BuiltinTools.cs
// Also https://github.com/HiddenMonk/Unity3DRuntimeTransformGizmo looked interesting (a move gizmo)


// See https://docs.unity3d.com/ScriptReference/MenuItem.html

#if UNITY_EDITOR

namespace OrdinaryCartoonMaker
{
    [MenuEntry("Mark Object Position", MenuPriority.CustomTimelineActionSection.start)]
    public class MarkAnimatedCharacterMenuItem : TimelineAction
    {
        public static bool markedPositionSet = false;
        public static Vector3 markedPosition;
        public static AnimationTrack markedPositionTrack;

        public override bool Execute(ActionContext context)
        {
            var track = context.tracks.First() as AnimationTrack;
            var binding = context.director.GetGenericBinding(track) as Animator;
            markedPosition = binding.transform.localPosition;
            Debug.Log("MARKING POSITION");
            Debug.Log(markedPosition);
            markedPositionSet = true;
            markedPositionTrack = track;
            return true;
        }

        public override ActionValidity Validate(ActionContext context)
        {
            if (!context.tracks.Any())
            {
                return ActionValidity.NotApplicable;
            }

            var track = context.tracks.First() as AnimationTrack;
            if (track != null && context.director != null)
            {
                // TODO: Really should be cleared when selection changes to a different track.
                if (track != markedPositionTrack)
                {
                    markedPositionSet = false;
                    markedPositionTrack = null;
                }

                var binding = context.director.GetGenericBinding(track);
                if (binding != null)
                {
                    return ActionValidity.Valid;
                }
            }

            return ActionValidity.Invalid;
        }
    }

    [MenuEntry("Move Object Position", MenuPriority.CustomTimelineActionSection.start)]
    public class MoveAnimatedCharacterMenuItem : TimelineAction
    {
        public override bool Execute(ActionContext context)
        {
            var track = context.tracks.First() as AnimationTrack;
            var binding = context.director.GetGenericBinding(track) as Animator;
            var deltaMovement = binding.transform.localPosition - MarkAnimatedCharacterMenuItem.markedPosition;
            Debug.Log(deltaMovement);

            Undo.RegisterCompleteObjectUndo(binding.gameObject, "Move animated object position");

            var originalTrackMute = track.muted;
            track.muted = true;
            TimelineEditor.Refresh(RefreshReason.ContentsAddedOrRemoved);
            
            binding.transform.localPosition += deltaMovement;
            
            track.muted = originalTrackMute;
            TimelineEditor.Refresh(RefreshReason.ContentsAddedOrRemoved);

            return true;
        }

        public override ActionValidity Validate(ActionContext context)
        {
            if (!context.tracks.Any() || !MarkAnimatedCharacterMenuItem.markedPositionSet)
            {
                return ActionValidity.NotApplicable;
            }

            var track = context.tracks.First() as AnimationTrack;
            if (track != null && context.director != null)
            {
                var binding = context.director.GetGenericBinding(track);
                if (binding != null)
                {
                    return ActionValidity.Valid;
                }
            }

            return ActionValidity.Invalid;
        }
    }
}

#endif

Line 102, should probably should also add "binding.localPosition != markedPosition" so menu item only appears if character is moved.