How to use iPhone to Store and Organize Photos Outside of Photos Camera Roll
Solution for that and as a side benefit, keep the "Camera Roll" as close to empty as possible (made a little compromise to accommodate keeping media original that has effects e.g. live, animated photos).

Need a photo organizer that:

a) stores photos/videos in it's on file space on the iPhone and can make albums from that source (so that it does not rely on "Photos").

b) is able to add photos/videos to that file space from the iPhone's "Photos" and be able to load photos/videos from any source so that everything is in one place (from which albums can be made).

To keep everything in original form, no transformations, here’s a strategy that will even work on an iPhone 5.

One compromise: to preserve the ability to play "live" photos or photos with effects, leave those in "Photos" so unfortunately, that means the Camera Roll would have some media in it.  Yes, one could compromise and let "live" photos get transformed into a .jpg and an accompanying .mov file but, the goal is to not transform anything and retain the exact characteristics of how the media plays so, if that’s important to you, leave it in "Photos".   fyi "Live Photos" and "Animated" photos are identified under "Media Types" in "Photos".

Photo organizers considered: Adobe Lightroom Photo Editor, Utiful.

Adobe Lightroom Photo Editor (free version does everything required).  Lightroom copies media into itself (it's own file space) and once it's there, you make albums that references media in that file space and therefore it will not be referencing media stored in "Photos".

To aid in getting media to the iPhone, install AirMore onto the iPhone (it's free).  AirMore serves two purposes: to transfer media to the phone, to serve as a single spot to copy media onto the iPhone which Lightroom can get at and copy the media to itself.

GETTING YOUR MEDIA ONTO YOUR iPhone.

1) Media that's on a camera.  Transfer it to a computer, use iTunes or AirMore to get it onto the iPhone.  Because AirMore's file space shows up in iTune's "File Sharing", you can copy files to that app without having to use iTune's sync.  Lightroom will be able access the file space in "AirMore" to copy the media into itself.

2) Media that's on a computer.  If you like iTunes and the computer has it installed, that's an option (copy the media to AirMore via "File Sharing).  If it isn't available, then use AirMore.  Regardless, both result in the media going to AirMore's file space where Lightroom can copy it into itself.

3) Media that's on an iPhone.  Use AirMore or Airdrop.  Airdrop is ideal for a specific scenario, for transferring "Live" photos or "Animated" photos from "Photos" because using Airdrop results in a direct transfer from one iPhones "Photos" to the other iPhones "Photos" and the media's effects are preserved.

Lightroom can now copy media into itself because it can access the files in AirMore.  Copy the media and delete it once it's copied. Lightroom can copy media from the "Photos" camera roll into itself.  Delete stuff that's been copied from "Photos".

Everything is original and in one place (except live/animated photos) in Lightroom.  The camera roll is as close to being empty as it can be.  Enjoy, get going on those albums!