Mac Pro (Late 2013) won't wake from sleep after High Sierra 10.13.5 upgrade

I have a MacPro (Late 2013) - aka the Trashcan, aka MacPro6,1 that won't wake up from a deep sleep. It also has lost it's ability to light up the ports on the rear - even when the Mac Pro is switched on, the power button doesn't have a light on it.

I’ve done some searching and can’t find much about this issue, but I have here in front of me a trashcan MacPro6,1 and it looks like the SMC is not responding.

In addition, when I move it, the ports at the rear don’t light up (as they usually do). If it goes to sleep for a short amount of time (I don’t really know, minutes to an hour maybe?) I can wake it, but if it’s left to sleep for a couple of hours or more, I can’t wake it at all.

Pressing and releasing the power button doesn’t do anything, tapping keys on the keyboard or moving the mouse doesn’t do anything.

I have seen Mac Pros previously (a couple or more years ago) that wouldn't turn on the display after waking from sleep - in this case I'm able to tap some keys on the keyboard to wake the machine (with a black screen), enter the login password and then press Ctrl+Cmd+Eject to reboot. The Mac Pro would then reboot and the screen would turn on. this is not an option with this new issue - the machine is completely unresponsive.

Seemingly the only solution is to force it to power off and on again.

I’ve tried zapping the PRAM (3 times for luck) and tried resetting the SMC (remove power and leave for 15+ seconds) and there is no change. In desperation, I’ve reinstalled the OS with High Sierra 10.13.5. It may be a coincidence, but I didn’t have the issue prior to installing the 10.13.5 update, 10.13.4 was OK.

Can anyone suggest any other troubleshooting steps that I haven’t tried?