So my question is: how can I achieve this in an acoustically correct way directly in Organteq, rather than mangling the organ by cutting frequencies, collapsing parts of it to mono (except for very low end of course), etc.?

It seems that one possible approach is to adjust the relationship between Stereo Width and C/C♯ Separation, since there is a interaction between these two parameters and this does help to some point. The problem is that I don’t know how to approach this systematically and acoustically correctly. There may also be other factors involved besides these two parameters, such as the parameters of the individual pipes themselves.

What I need are some basic rules or algorithms, even at a conceptual level—for example, "the higher you set parameter X, the lower parameter Y should be" or "the higher is parameter X for one stop/pipe, the lower it should be for another stop/pipe".

Do you mean that the left and right channels show a low or negative correlation in the correlometer, and that you therefore consider this undesirable? Or do you mean that two different pipes/stops playing together are cancelling each other acoustically because you believe their waveforms should ideally be phase-aligned?

I’m asking because, in a real pipe organ, two pipes or two stops are not necessarily expected to be “in phase” with each other. Their physical positions, propagation times, spectra and radiation patterns naturally produce frequency-dependent phase differences. In particular, an 8′ stop and a 2 2/3′ stop playing the same key are not simply two copies of the same waveform that should be phase-aligned.

So I’m curious: what is your reference for deciding that the phase relationship is “correct” or “incorrect”? Is your goal to reproduce the physical/acoustic behaviour of a real organ, or is your goal to maximize stereo correlation/mono compatibility?