osmc@RASPI2:~$ uname -a
Linux RASPI2 4.4.16-1-osmc #1 SMP PREEMPT Thu Aug 18 16:30:00 UTC 2016 armv7l GNU/Linux
It took nearly five hours to build, but at least I built my first (custom) kernel, yay. 
Btw, it worked with an 8 GB µSD card that contained nothing but OSMC.
Before I started building, I edited the /home/osmc/osmc/package/kernel-osmc/patches/rbp2-000-add-kernel-config.patch to contain
+CONFIG_JOYSTICK_XPAD is not set
+CONFIG_JOYSTICK_XPAD_FF is not set
During building some y/n/m questions came up for including stuff into the kernel, I answered n to CONFIG_JOYSTICK_XPAD and CONFIG_JOYSTICK_XPAD_FF. Also about six questions about sound broadcom thingie (unfortunately didn’t take screenhots) to which I replied n as well.
sudo dpkg -i rbp2-image-4.4.16-1-osmc.deb, edited /etc/osmc/prefs.d/update_preferences, removed the sudo rmmod xpad line from /home/osmc/start.sh, rebooted, tested controller.
Unfortunately it still doesn’t work reliably. All tests/methods from the last ten posts above showed the same behaviour and error messages.
Now it might be imagination, but with the new kernel it worked in 4/5 cases. What also changed was the LED behaviour; now flashing always means working, and staying lit in position 1 always means not working. This is strange, as this is exactly what the --led=2 in /home/osmc/start.sh tells it to do.
Therefore I still think it can’t be a problem in principle but has to do with the order or way the USB device is initialised. If this can be determined by syslogs or anything, I’m happy to provide them.