Thanks very much Paul! I really appreciate you taking the time to help me.
I have followed your advice and it seems to have worked - I'm no longer getting the 'DNS error' message in my SquareSpace settings.
However, one question: I still have an A record in my 1&1 settings with a host name 'ftp' that goes to the old SS address. Should I just delete this or do I need to do something else with it?
(Incidentally, the guides you linked to seem to be written as if you are connecting a new domain, and don't tell you how to edit the DNS records on a domain that is already connected, hence why I was stuck. I can't see the 'new' IP addresses you list for SS anywhere in those guides for instance.)