Actually I tried to make some changes with Disk Director with no success so I am now doing it with Easus Pro (which I forgot I have) and it seems to be working fine. It's going to be a lengthy process (shrinking 1 partition, moving 5 partitions, increasing free space on system partition) but I'll report back when it's (hopefully successfully) finished.
Oh - and where Acronis said it would need to boot 5 or 6 times during the process, Easus seems to be doing it all in one step!