Further reports – for whatever it is worth …
– Downloaded the Jessie image from adafruit: The display works flawlessly
– Downloaded fresh M2P-image. Installed the Touch-Display Plugin (Link): Nothing.
– Installed the display again, as in the instructions for older kernels: Still nothing.
– Configured Jivelite, updated it to the newest version: The screen blinks momentarily but stays black.
– Installed VNC and accessed the Pi remotely: I see Jivelite and can configure it on my PC. On the Pi, though: Nothing.
What else could there be to do?
2 hours later: I now use the m2p image with the adafruit installed manually (not via m2p). This way the screen works as expected and since I found a way to adjust the screen via VNC I now have a system that functions to my satisfaction.
Strange though, what is going on with the plugin here …
I now consider the problem solved and I will put the Pi in it’s intended space in my car now.