My last post got garbled by the system! I shall try again to post the message from the Bug Reporter engineers.
'Time Machine intentionall yields to other processes in the system trying to do IO or CPU intensive tasks. The diagnostic shows that Time Machine is heavily IO throttled because of all the other processes doing IO on your system. Most of the I/O seems to be coming from "Sync Folder Pro", but there is also significant IO from dropbox, Adobe Creative Cloud, and Clam AV (which is scanning files being synced by Syn Folders Pro and dropbox possibly?)
It's hard to tell if Sync Folders Pro is just busy or malfunctioning.
I'd suggest trying the backup again when your system is less loaded. If you continue to have problems please try disabling Sync Folders Pro and be sure that your AV software is not scanning your backup destination drive. (You might want to experimentally disable the AV software and see if that helps as well).'
So I turned every running application off and started a new TM backup, submitting several sysdiagnose files to Bug Reporter during its duration. 'Preparing Backup' lasted for nearly 6 hours. Then 'Backing up' began, became extremely slow at one stage, then accelerated madly to a finish about 3 hours after starting. As far as I can tell, the backup is complete.
It is clear from this whole discussion that TM's behaviour or misbehaviour varies hugely from one user's computer and its contents to another, but it does seem that, as indicated by the engineers' statement which I have now succeeded in copying and pasting (above), turning off applications — and especially other file-copying and transferring applications — may be the way to go.