Q: Photos Library - Very Large

I have around 30k images in my Photos library and recently used PhotoSweeper to eliminate duplicates.  I also deleted an iPhotos library I hadn't realised was still there.  This freed up an enormous amount of storage.

There are people here with much larger libraries than yours and don't have any problems. There should be no problem using an external drive and no need to start using symbolic links.

Personally I think a communal family album is undesirable. Not only does it mean others might see photos that others don't want them to see, but it also means that everyone is able to delete or alter anything either intentionally or in error. Furthermore, everyone also has access to your mail, contacts, diaries, messages and the like and just like they can with your photos they can also delete and alter this data too.

And Photos on the OS X doesn't have all of the features now on the phone (people, places, things).

Incorrect.

We each have separate iCloud accounts and thus have separate logins on the "home" machine

Then you won't have the issues I suggested with contacts etc but it's even more complicated than I'd imagined. Obviously it's up to you but I'd just have separate libraries and forget all the rest. Use the family sharing album with family iCloud set ups if you want to share some photos between you all.

I would still have to have (somehow) each person's Photos library on a NAS/external device.  But Photos will only permit iCloud Photos from a library in the ~/Pictures folder.

That's incorrect, you can use an external drive in just the way I mentioned above.

Well, let me rephrase:  Searching for Beaches on my phone gets 222 results (more or less correct) on Photos I get 4.  The same for other categories.  My guess is that because of the sync errors with Photos it isn't as up to date as it should be.

Each device finds it's own faces etc so yes there is the potential for some difference but I suspect yours is more likely because everything has (seemingly) gotten in a mess.

Another issue is when we attempt to turn on "iCloud photo sync" on our phones, we get a dialog something like "To turn on sync 8,700 photos will be deleted from your phone".  This isn't what should happen, iCloud sync should literally sync what is already in iCloud Photos and what is on our phones.

This sounds like you have previously been syncing with iTunes, the photos it will be removing are the ones from iTunes not the ones that are in the phones photo library, you can't sync with iCloud and iTunes at the same time, so your iTunes photos are removed, this is expected behaviour.

Stop messing with an NAS - Photos will not work with it

Multiple libraries is not a solution - as usual anyone can post anything on the internet and often it is total BS - multiple libraries are confusing and lose the search power of Photos - you will import photos to the wrong library and never be able to find the photos you need quickly

the best solution is iCloud Photo Library with optimized photos on devices with limited storage and at least one large Mac with adequate storage for all originals to have everything and do the backup there

Alternatives would be to use a local external hard drive formatted ac OS extended (journaled) or to change to another software program

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I have a MBAir with 256GB and iCloud Photo Library.  I've run out of space on my HD and can't import any more photos.  I'm thinking I should move my whole library to an external HD, but am not sure of how to do that properly.  What does your comment "formatted ac OS extended (journaled)" mean?

It means exactly what it says - to use the  photos library on an external drive the drive can only be formatted Mac OS extended (journaled) - you can format it using disk utility (in your utilities folder in the applications folder) purchase one that is correctly formatted

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