Hi again. Ok, I may have discovered a work-around to this problem.
This morning I went to wake my (27" late 2012) iMac (OS 10.13.6) but it would not wake. I have Power Nap enabled, as this has been suggested may be good practice for the SWF... and for the last few occasions this seems indeed to have made a difference. However, today it would not wake.
I wondered if I were to press the space bar (or any other keys) for a time then, because Power Nap is enabled, the Mac would "wake" during one of these presses (to check for mail or whatever) and "know" that it's being asked to wake.
No joy.
It then occurred to me that if I were to give it a real jolt, then that may be sufficient to wake it. So I plugged in a USB-powered drive... and hey presto, the Mac burst into life.
This only happened this morning, so I haven't repeated the experiment - thus I only offer this as a possible solution, and would be interested to hear if it works for others. Please let me know. Thanks.