Is there a reason you haven't tried Apple's iCloud? It does cost a bit-- 50GB is $1/month and 200GB is $3/month, but the service allows you to keep small copies of your pictures on your phone while the full sized versions are at iCloud, albums and folders intact. You can view, edit, and print the pictures from your phone, and full sized versions will be imported as needed. It's all quite seamless and secure. And you can share chose pictures with others.
I was reluctant, at first, but iCloud Photos offered a number of features that I'm finding to be very useful. You can read about it here:
Set up and use iCloud Photos - Apple Support
iCloud isn't exactly a backup-- it syncs your devices. But it will allow you to free up storage on your phone without losing their availability.