The experiments and thoughts described above helped me to shift my focus. I would mostly end my improvisation practice session by playing a longer solo for the camera. During this mini-performance I shift my focus using the ideas described above. I afterwards found myself focused more on the atmosphere, the movements I made and telling a story.
As described in a multidisciplinary research led by David Dolan and John Sloboda there is a thing such as the improvisational state of mind. As a research experiment they had a chamber music group perform the same program twice: once in 'strict' mode and once in 'let go' mode or the improvisational state of mind. In the strict mode the focus was more on the technical details of music making such as doing all the right dynamics, good intonation, making the performance as expressive as possible, etc. The let go mode is more about playing freely, expressing themselves spontaneously and absolutely no focus on 'not playing wrong notes'.
As an exercise I tried to apply an idea by violinist Sarah Stiles. She calls this exercise alternation between tranquility and disturbance. Normally it is performed as a duet, but I found it also has value as a solo experiment. The improvisation is started in a calm atmosphere, and then suddenly disturbed with loudness or sharpness. You can alternate both atmospheres a few times before ending the improvisation.
As in exercise 2 from the Connecting Ideas-pool, it could be a good mindset-experiment to start with a written out first half of a sentence based on a certain piece and finish it improvising. This has to be done multiple times. The challenge is to make each time completely different. This exercise was suggested by Bert Mooiman. This way the focus of the player goes more and more to the expression and variety instead of the musical material previously studied.
Both exercises above help to experience the improvisatoinal state of mind. The final step should be to add this improvisational state of mind to the interlude itself. This could be simply done by just trying to let go. For me it could help to close my eyes, focus on the feelings I want to express, letting my body move. So taking the focus of the content of my improvisation.
When showing the following video to my peers, I generally got the feedback they could hear me think too much. I found myself worrying about the content of my improvisations. My thoughts were with the notes, chords, modulation: