Just in case anyone has arrived here with the same question/problems as me I thought I'd give the best solution I've found since making the post. I'd really appreciate hearing from anyone if you have a better or easier method.
1) I open the note and click the 'share' button to send it to Reminders. I open Reminders, select the new note and then 'Add Date'. So far, so good, (as before) and this is now a really useful tool when you want to remind yourself of a task but can then click on the link to go back to Notes for any complicated instructions or info, for example.
2) To keep a local backup of Reminders I go to File, Print, Save as PDF. This gives a document of a simple list of reminders with dates underneath. But the links icon has disappeared so there is now no way to get to the useful info that you hold on Notes app. IF the info you want to access is brief then you could add it to the reminder where it says 'Notes' at the same time as the date but in my case that is not convenient as the link might be to a copy of a whole web page. However, as the reminder title is the same as the note title it is quite easy to find the info again if needed. In fact you can even save the PDF file as a note itself and have it at the top of Notes app, although there is not much point.
3) So you now have to have confidence that you have an accessible route to recover your notes if you should lose them, and Apple doesn't really provide this either. So I have found a simple app called Exporter available free on the App Store. It saves all the notes as individual files in alphabetical order in a folder. It doesn't save links in the notes, but then neither does iCloud. If you don't have many notes with links then you could go through them before export and manually convert the links to text.
All a bit clunky, but at least everything is saved and can be recovered with a bit of effort. Of course what is really needed is for Apple to enable Reminders and Notes on Time Machine to back up with clear labels and instructions for recovery of app contents.