Again you can read my mind and understand it better than I do...
Trying out all these functions of a button I'd like to create makes me stumble over all kinds of little issues whenever I thought I nailed something, so in this case, following your suggestions on earlier questions, I felt like I needed the state of mouse_entered/exited "remembered and forgotten" at the same time, which wouldn't work.
So I came up with a combination of my earlier approach of a "run-until-the-end-timer" and your suggested "quit-when-release-timer" and... nailed it! (For now.) I uploaded an example here: https://we.tl/t-SUiz37CsN2 so please feel free to check it out (and optimize to your liking if you want to : )
What I had a hard time to solve in the end was occasional inputs outside the Area2D and signals automatically following yields where they shouldn't etc., but now everything seems to work just fine. It's hacky without a doubt and I am absolutely sure that there are much more elegant ways to achieve the same result, but my beginner-ambitions certainly are very satisfied for the moment.
On to the next challenge! (Which will be this functionality put on a checkbox-button...)