I have done some more testing and the plot thickens a lot.
I tried the apsync image and raspbian on a brand new RPi3 B+ and an older RPi 2 B. I tried two different SD cards (both taken out of perfectly working RPis) and flashed using different tools (dd in linux and Win32DiskImager in windows 10).
It seems that the apsync image flatly refuses to boot on the RPi 3. When connected to a display, it shows the rainbow screen and the lightning bolt icon indicating power issues. However, power seems highly unlikely to be the problem since I am powering it via a 2.1 Amp wall adaptor that works fine with other RPis.
The same apsync flashed SD card, boots fine on the older RPi 2 so the card is not the problem.
Also, I tried a freshly flashed Raspbian on the RPi3 and it boots fine so power is not a problem either and the RPi 3 board is fine (I thought perhaps I had bought a defective board).
So, individually it looks as if card is OK, power is OK, board is OK but the combination of those (RPi 3, latest apsync) refuses to boot. I also tried the adding “boot_delay=1” to the config.txt file trick but no joy.
So, any ideas what I might be missing? The latest apsync for the pi was uploaded on Oct 5 2017 so it seems extremely weird that nobody would have run into problems before.