What many people don't understand (because Apple hasn't promoted it well) is that you can put your photos into "Shared Albums" and then delete them from your photos app. Note: This doesn't solve the issue of backing-up, but does solve the space issue.
You can put an unlimited number of photos in Shared Albums (I have many thousands) and you don't need to share these albums with anyone. They just reside on Apple servers and you have access to all of them as long as you have a wifi or cellular connection. You can, of course, share these albums with your wife, family members, friends as well and they can comment on them or add their own photos.
On a recent trip to Disney, I shared an album with my wife and grown kids and all of us added photos that we took during the week. There are over 1,000 photos now in that album and all of us have access to them anytime. But, as I said, you can also create a Shared Album and not share it just to remove those photos from your phone. These albums are available with all iOS and Mac devices including an Apple TV.
Now, you still need to find a good back-up plan, but this is a great way to have almost unlimited space at no cost. (BTW, you can upload 25,000 photos per month and share up to 100 different albums.) Here is more info:
https://support.apple.com/en-us/HT202299
Periodically, I export all my photos that reside on my Photos app (using my Mac) and then back them up to a second drive. I use lightroom for pics from my dslr, but I realize that you don't have that option for now. You can use wifi (depending on your camera) to move your pics from your DLSR to your phone or iPad and then upload them to Shared Albums. Hope this is not too confusing.