Photos backup strategy before deletion from iCloud/iPhone

Having successfully completed the task, I thought I'd summarise what we ended up doing in case it is useful for others. Note that we were doing this from a new MacBook Pro with just 128GB of SSD hard disk space, so at no point could the computer store full size versions of all the photos. Things may be quicker and easier if you have a larger hard drive, but the basic steps will be the same.)

The steps we took in the end were as follows:

I've looked at various strategies for doing this and what I propose is this:

1. Open Photos app in the default library (i.e. the current System Photo Library). Select all photos and export to a folder on an external drive. This is time consuming but provides peace of mind as a backup of all images in case something goes wrong with the following steps. The export settings used were as shown in the screenshot below:
   
   
2. After the export was complete, close the Photos app. At this point I attached a separate external drive for extra security though this is probably not necessary. Whichever way you go, make sure the external drive has ample free space – our library of about 20,000 photos and videos ended up being about 200GB. Also make sure you have ample data available on your internet service as most of that 200GB, or whatever it is, will need to be downloaded at step 7.
3. In Finder, navigate to the Photos Library in Pictures and copy it to the external drive.
   (Note that there is no point trying to ensure that all photos and videos have downloaded to the Mac before this step, as it will happen at the next step anyway. We found that even when it said all photos and videos were downloaded, they actually were not. Also, exporting the photos does not necessarily leave full sized versions in the original library.)
   
4. Open the copy of the Photos Library (the one on the external drive). (I renamed this beforehand to 'Photos Library - copy' to avoid confusion.)
5. Open Photos > Preferences. In the General tab, click 'Use as System Photo Library'. You'll be warned that switching the System Photo Library will turn off iCloud Photo Library. Click 'OK'.
6. While still in Preferences, click on the iCloud tab. Check the 'iCloud Photo Library' box and select 'Download Originals to this Mac'. That last step is very important. Close Preferences.
   
   
7. Now wait. Unless your original Photos Library already contained full resolution versions of your images, they will now download. This took us about 24 hours and nearly 200GB of data – on a relatively high speed connection. Best just set and forget. You can do other work while this goes on in the background, but make sure you keep the external drive connected, the Photos app open and your computer awake. At the very bottom of the Photos screen you should see a progress bar indicating the, well, progress of the downloading. We also found a small number of (mostly) videos that somehow had got lost from iCloud so Photos wasn't able to download at all.
8. Once that the downloading is finally complete, you will have a complete version of your original Photos lbrary including high resolution versions of the images.
9. Now you want to make the original library (the one on the computer) the System Photo Library again. To do this, close the Photos app, navigate to the Photos Library on your hard drive and open it. Open Preferences. On the General tab, click 'Use as System Photo Library' (as in Step 5, again saying OK to the warning), then on the iCloud tab turn on iCloud Photo Library. In our case, because of the very small hard drive, we chose Optimize Mac Storage on this occasion.
   You should now be free to delete as many images as you like from your main photo library (either in Photos on your Mac or on one of your connected devices). However, as a precautionary step I wanted to check that the backup library was working.
10. Close Photos again, navigate to the Photos Library copy on your external hard drive and double click on it to open. In our case we were warned that the library contained some (a small number of) images that couldn't be downloaded and that these would need to be deleted from the library. There is no choice to say OK to this or otherwise quit out of Photos, so say 'OK'. It will now take some time for the library to cleanse itself (perhaps a couple of hours) but it should eventually open. I then ejected the external hard drive and connected it to another Mac, then opened the backup library on that Mac. I was now happy that the backup library was complete.
11. Now it is definitely safe to delete any or all of your images from the original photos library that resides on your Mac and in iCloud. If you want to make space on, say, your iPhone, don't forget to also delete the images from the Recently Deleted album. You can do this safe in the knowledge that you have all your images backed up outside Photos (from Step 1) and a complete, offline backup Photos library as well which retains all the structure of your original library.

I hope all that makes sense. It's a complex and time consuming process (and it would be nice if Apple made it easier) but I now know that it is possible to make space on a phone (and/or on iCloud) without losing original images.

Thanks for your insight Léonie. I'm wondering if it would work to add an extra step between 1. and 2. above and export all the images from the existing library before duplicating it, as a 'backup of the backup'. Obviously this would take time and disk space, but I assume if you export, Photos will download any undownloaded images as part of the process in order to export full-size versions. I know from past experience that export is less than ideal as a way of backing up as you lose all the file structure, and of course only end up with edited files, not the originals as well. But at least it would provide surety that we have a full-size version of every picture just in case.