I wrote my Master Thesis on partially coherent classical wave fields applied to gratings, so I will try to give some insight on what exactly about the double slit makes it a quantum problem and what is really just classical wave mechanics. This should simplify the discussion a bit by separating the two issues (at least hopefully).
General comment on the double slit
In my opinion most of the properties of the double slit that are usually attributed to quantum mechanics can actually be perfectly reproduced with classical wave fields from statistical sources. By that I mean e.g. an electromagnetic field that has some statistical phase-fluctuations due to the source process. Most light can actually be represented in that way in particular from astronomical sources. Even some laser processes can, since the notion of coherence can easily be formalized as statistical correlations of the wave field (1). The only regime where this breaks down (to my knowledge) is the few photon limit and some non-ergodic processes/pulses.
With this approach you can get everything you want when thinking of the double slit experiment:
- Interference pattern on a screen for sources with small angular and wavelength spread
- Coherence can be modelled (2)
- You can couple to classical waveguide detectors ("observers" that are very well modeled classically).
Relation to the Question
The situation the OP described can also be created this way, with a purely classical "observer". Just put a fully incoherent re-emitter (something that absorbs the power at one point and re-emits it incoherently as a half-spherical wavefront. Not sure something like that exists, but a simple dipole antenna probably comes pretty close) instead of this "quantum observer". If you put it directly into one of the slits you will make the interference pattern disappear due to statistical phase fluctuation. As the observer is moved further away the pattern would change obviously, in the far distance limit it would go back to the original pattern. I can try a simulation of that since I have a program that does these kinds of things, but I think this qualitative insight should be sufficient for the question.
Where is quantum mechanics?
So why do people even talk about quantum mechanics when looking at the double slit experiment? Historically it was used to show that other particles (e.g. electrons) have wave-character. In the many-particle limit we could even describe that with the formalism described above. The only point where we get a problem is the few-particle limit. What people start discussing then is how the particle has a certain position when detected on the screen, which then leads to arguments about the measurement problem. I will not go into detail about this here, other people like @LubošMotl know a lot more about it than me and I suggest listening to their advice. What I wanted to emphasize though is that this is a completely separate issue from propagation through the double slit and the interference caused by it.
(1) see e.g.
- M Born and E Wolf. Principles of Optics. 7th ed. Cambridge University Press, 1999.
- S. Withington, D.J. Goldie, C.N. Thomas. "Partially Coherent Optical Modelling of the Far-Infrared Imaging Arrays on the Cooled-Aperture Space Telescope SPICA". In: Annalen der Physik (2013).
(2) see e.g. this answer of mine