I therefore would like to know, when this conditions can be relaxed...
When you are not writing a four part SATB chorale.
But, let's look at the actual concern about voice crossing. In the linked question about Tymoczko and voice leading the concern was voice leading efficiency not specifically prohibiting voice crossing. However, in that question, notice Richard's examples and how the voice cross involves only the inner voices and not the soprano. Such inner voice crossing are not normally a concern. That includes SATB chorales. Some textbook exercises may prohibit inner voices crossings, but you can consider that as a skill test not an actual part writing norm. In real music voice crossings often are done for the sake of giving the individual inner parts a more interesting melodic line.
Voice crossing over the soprano, or highest, part, is a special concern, because it can create the impression of a different soprano melody than what is written in a score. For example...
The first three measures show a soprano and alto together and then separately. A descending soprano and ascending alto. The four measure shows the effect of the crossing where the soprano melody is then perceived as a lower auxiliary motion instead of the written descending line.
However, there are two ways that perception can be avoided.
- Some kind of articulation of the parts so they can be distinguished. Playing one part louder than the other would do it.
- Play the parts with different instruments so the overlap isn't heard as one instrument. If those two simple lines in my example were played on, for example, a flute and guitar you wouldn't confuse which part is playing which line.
You example guitar score presents a complication, because there are rests and the voice counts change. This is how I labelled the "voices"...
The apparent crossing is the middle part in green "crossing" the top part in red. The only problem with that description is the top part is taking a rest at the one note of the middle part that crosses "above" the top part. Then the top part drops out of the texture. This can't really be regarded as a voice crossing, because the other part has disappeared.
I think the concern is whether this is perceived as the top part...
That potential is there regardless of any voice crossing. If the middle part did not go above the E4, we might have the same perception, because the part count changes. It could be the top part continues and the middle part disappears, or the top part disappears and the middle continues. The only thing making the distinction in the score is the eighth note rest and half note showing the parts overlapping in time. But, aurally that distinction in parts could easily be missed. The confusion of parts issue in this specific case is less about the voice crossing and more about the changing number of parts.
That covers the voice crossing question, but I don't think it gets to the heart of what you really want. I think your concern is handling harmony but not in a SATB, chorale, polyphonic context. You might look for keyboard harmonization books which treat harmony from the perspective of accompaniment. Figured bass was the historic practice, but you can find modern books that work with Roman numeral root analysis. The approach is more about chords - think block chord or chord pad - rather than SATB part writing.
Finally, it depends on what you are arranging. If the music is polyphonic, you do need to treat it from a part writing perspective and be concerned about crossing the top line. If the music is melody with accompaniment, homophonic texture, you can take the harmony as accompaniment approach and relax the voice crossing concern.
