I've been away for a week since my primary NAS died and in the meantime an identical unit has been shipped under RMA from Amazon. So today I began running through the recovery steps suggested on the Synology site. This wasn't quite as straight forward as I had expected (insert the drives in the new unit and off you go) but still trivial. Although I was confident that my data was safely backed up with multiple levels of redundancy, I was worried that some settings might have to be reinstated. As it turns out, I was relieved to find that following the migration the new unit was identical to the old one.
The steps to migrate to the new unit:
After that, everything was back to normal as if the outage had never occurred. Even my docker containers booted straight back up and carried on without a hitch.