Are there similar such Gedankenexperiments in continental philosophy?
The first one that comes to mind is Sartre's Le Regard (The Look). It is a very concrete thought experiment I would say (i.e. one that you could encounter everyday), which is very typical for existentialist philosophy; it is 'rooted' in everyday experience. It is, however, not an easy one and I would recommend reading his Being and Nothingness (you'll probably need a companion to fully understand all of his ideas). It will take a while to get through it, but it's worth it. I will try to summarise the thought experiment in a brief and concise manner, however, I do think it's full value only becomes apparent once you know more about Sartre's work.
Stage 1: alone
Imagine you are alone in the park. What do you observe? Lifeless objects (the grass, the tree, a bench,...); (être-en-soi: "being-on-itself") In this stage, you are the centre of a world; not just the spatial centre, it is more than that: the quality of things are merely what they appear to be in your eyes.
Stage 2: human being who does not see you
A human being enters the park, you see him but he does not see you. This man, however, does observe certain things just like you did in stage 1. He sees the trees, the grass,... He is, just like you in stage 1, a centre of a world. He sees certain things you see as well, for instance a tree. In other words, the fields of vision of you and the man intersect. Sartre calls this "disintegration", which can be defined as a decomposition of your world. However, during this phase, the decomposition is still controllable, since the things that have a reference to him, but that reference is also part of your world.
Stage 3: human being who sees you
In stage 2, the man was the object of your perception. Now, that man sees you. You become the object of his perception (and you're aware of it). You are, in other words, objectified by the man (être-pour-autrui; "being-for-someone-else"). This is not just his business, it affects you as well. During this look, the other one disappears as an object for you. It's not that you can't see him anymore, it's just that you cannot observe him anymore (his look conceals his eyes). The other now has the power over us: he can "define us". Are you ugly? Only if he thinks you are! Are you smart? Only if he thinks you are! etc. From this moment onwards, we can feel ashamed (this can only happen when we are objectified by another human being). This is what Sartre means by "hell is other people", contrary to how he is often misquoted (it is not a misanthropic statement!).
Is this a gesture (of fellowship) towards the experiment in scientific practice?
I wouldn't say so, at least not in this case. Sartre's existentialist philosophy's main concern is our subjective experience rather than objective factors that influence us. I consider it a way to make things clear to the reader; to understand and imagine things from his own, subjective conciousness.