i have an update on the topic:
i was not able to solve the problem, but out of curiosity i ordered one of the new raspberry Pi 3+ models and tried exactly the same i did with the old model and this time it worked!
Not out of the box of course, because the shairtunes plugin did not work at first, but after installing the bug fix the problem was fixed. Shairtunes is listed as working in the LMS plugin overview and i can stream music from my iPhone to my Squeezebox Radio.
But there is one problem still: when i stream music, there is a short pause every few seconds…