Woah, 
hugone! Just noticed your example with perspective jumper and was in... awe, mucho!!!!!!!!! 8-) Close to what I was intended, thanks.
you are welcome!
Tweens and Bullet: Bullet is dynamics, would not vote for it anyway, as it is suitable for different gameplay concept.
complete agree!
Why would you avoid LiteTween? I thought that LT would give more intuitive control over trajectory adjustments, like for variable jump heights, quicker to set up.
well also true depending on the case... as I showed to you lerp do the trick with complete control over the animation (or trajectory, etc), depending on the case.
in general, in my modest opinion, if you could do anything not using third party plugins (as is this case), the better. In the past, I was a huge fan of any new addon/plugging and I was using it even if it had no sense to do it.
Example: you were using the tween for both objects, the BoxChar and the Shadow... this could lead to problems (you got two independent procedures that you will have to sync) and when the game gets more complex you can end up with performance issues. As you can see in the example the shadow do take values from the BoxChar.. so you don't force the CPU to make extra work (when the game is not still complex there its not problem, but if you don't plan it good, then eventually may happen that you will expend more time optimize than doing it)
tween its really nice to use too, especially it's so simple to use it in bounces, etc... in very strict 2D, but for this special case (where you have to combine and concatenate tweens) it will be more a headache than a help.
I like your Case (move) branching, makes entire code more structured.
well, in my example I don't like that I used global variables for everything (I used for the initial screenshot before you updated C2 to show all in one image)... if it is about the movement of the BoxChar I advice you to make an instance variable of that object (move,startX, etc). That way will look even more clear when you got much more objects around.
Is this still hardware independent, since you use dt increments?
yes using dt you got the hardware independence.
Your example made me completely reconsider my approaches to the code, as I naively thought that everything must reside under everyTick. I will post an update with what I ended up. Gracias!
I am very happy I show you another way of doing it! es un placer amigo!