Ok I tried to implement what I wanted starting with a Tweener, using a property and then running a DOTween.To on that property value. But it seems, that the Tweener does not read the value, but has a copy of it.
SetTarget gave me the impression of "setting a new value target", but instead it's used to change what the tweener is working upon.
So no luck at this point, I wrote my own script for this one not using DOTween.