Brand-new iMac 5K random reboots

I'm a "veteran" Mac user (since 1994), however, the recent behaviour of my late 2015 iMac 27" 5K has me at my whit's end:

Right after the initial install and set-up, the iMac started randomly rebooting at night time. (It was always left idle, never sleeping.)

The only "smoking gun" I could find was this:

localhost kernel[0]: Previous shutdown cause: -128

I have talked to AppleCare a couple of times, my case has since been pushed up to their 2nd level support. So far - no solution found.

Here are the things I have tried (I believe me, I have...):

• Reset the SMC
• Reset the PRAM
• Chucked most of the LaunchAgents and LaunchDemons
• Re-installed Mac OS X 10.11.3
• Set-up a new, blank "test" user and re-booted into Safe Mode
  • Even in the "Safe Mode", weird things happen: After sitting idle (as the "test" user) for a day of two, the iMac "locks up" i. e. the screen stays blank and neither mouse, nor keyboard nor "Power On" button on the back of the iMac manage to wake up the machine.
  • Also in "Safe Mode" I get truckloads of these:
    [watchdog_daemon] @( wd_daemon_init) - could not open connection with the kernel watchdog

Short of "nuking & paving" the machine, has anyone got any ideas what could help?

Or does this sound like a hardware bug?

Any help appreciated,

greetings from Berlin,

jan