I'll pull my remarks from the (now migrated) comment thread in, since this has yet to be properly addressed. To answer your main question,
has this "thought experiment" been simulated by solving numerically the underlying Schrödinger equation?
I would say:
- the precise simulation you propose (or close variations of it) probably has been performed at some point (probably multiple points, by multiple people);
- it probably hasn't been published;
- if it did get published, it won't make for a particularly interesting paper; and
- if it hasn't been published, it's a mountain of a task to show credibly that there is no such paper in the literature.
Now, the reason for the above is that the simulation you propose just isn't very interesting. You say that
Its interest could be in particular to better understand in which precise way the observation progressively becomes inoperative when the photon wavelength increases.
but that is not the case: anything that such a simulation could show us, we already understand.
It is well understood, since the days of von Neumann, that within formal, unitary quantum mechanics, the effect of measurements is to cause entanglement: if the system is in a superposition of $|A=1\rangle$ and $|A=2\rangle$, say, and you measure $\hat A$, with some detector that goes to $\left|\uparrow\right>$ on $A=1$ and to $\left|\downarrow\right>$ on $A=2$, what you're really generating is the superposition
|\Psi\rangle = \alpha \left|A=1\right>\left|\uparrow\right> + \beta \left|A=2\right>\left|\downarrow\right>,
i.e. an entangled state between the system and the detector. This state can no longer show interference, because if you take the inner product between the two components, i.e. if you do
\bigg< \left|A=1\right>\left|\uparrow\right> ,\, \left|A=2\right>\left|\downarrow\right> \bigg>
= \left<A=1|A=2\right> \left<\uparrow\middle|\downarrow\right>
you get zero, because the detector states are orthogonal. This completely kills any chance of interference, but the wavefunction hasn't "collapsed" (yet); if you do a projective measurement on the detector (forcing its wavefunction to "collapse", whatever that means), that extends to the system as well, but that is external to the simulation.
Let me reiterate the point: anything you could simulate, while keeping to unitary quantum mechanics, would completely fit within the scheme above, and it would not add to our understanding of the thought experiment.
If you do want your simulation to include some form of wavefunction "collapse" (or decoherence or whatever you want to call it), i.e. if you want your simulation to actually say anything useful about the measurement problem, then you're going to need to decide how you handle the information encoded in your which-way detector, and this is where your scheme goes south: in order to simulate anything at all, you essentially need to pre-bake some resolution of the measurement problem into your simulation. Whatever results you get back will just be a restatement of the premises you feed in, and will be subject to all the flaws of the premises.
Given this, all that such a simulation would provide is a very expensive visualization aid for processes that can already be understood analytically, and for which the main difficulty is conceptual. The creation of visualization aids is not without merit, but this one would offer very little towards the resolution of the true conceptual problems of the measurement problem, which have much more to do with what projective measurements mean than with photons and double slits.