So you have two qualities you're looking for in a martial art:
It shouldn't put you in a position where you have to really fight your way out (because you have an injured back that won't be able to heal unless you lay off it).
It should be effective against someone who doesn't cooperate - i.e. someone who actually fights back.
The problem, as you saw for yourself, was that styles that are good with #1 are never going to be good at #2, because they never actually try to spar against people who aren't cooperating.
And vice-versa, styles that are good with #2 are never going to be good at #1, because those style necessarily have to put people in positions where they have to struggle to get out of holds and such.
Most but not all styles like Bujinkan ninjutsu, classical jujitsu, aiki-jujitsu, aikido, etc. do not practice with non-cooperating partners. They like to think they do, but they don't. Their version of non-cooperation involves partners who stand there letting you do an armbar on them, but maybe they'll keep their arm tense until you strike them in the lower ribs or something, and then they'll let you have the armbar.
That's not the same as someone who's going to prevent you from even getting close to being able to apply that armbar. And when you do, they'll just do a level change on you to get a single leg take-down while you're doing it. That's a completely different ballgame.
Unfortunately, that choice is what you're up against. You can have one but not the other at the same time.
And by the way, you could suspend your judgment for a while and do a classical jujitsu school to learn their techniques. If you go into it with the mindset that you know this isn't going to work for real against struggling opponents, and that you're just there to learn something new, then you might find that it can be very enjoyable.
You may even find a hidden gem that you can take back into your BJJ / MMA practice when you return to it someday. It's not the techniques that are the problem. It's the way they train that matters.
One word of caution, though: Classical jujitsu styles, Bujinkan, aikido, etc. are not gentle arts (haha). They can involve back-wrenching practice. So you have to be careful even with them.
Which brings me to another question: Why not try going back into BJJ/MMA, but make sure your instructor and partners all know you can't go all out and may need to tap instantly if your back is being put in a bad position?
I guess you're not confident that you can do that with BJJ/MMA, but you're okay with classical jujitsu. That's fine. Just throwing out the possibility.
Maybe, though, the best thing is to just let your back recover and not risk doing anything to harm it for a while. It sucks to realize that, but this might only keep you out for a year or two. You have the rest of your life to do martial arts. Spend that time maybe working on basic exercises like weightlifting and running. It won't be wasted time.
And heck, if you really want to do something that's still a martial art but is good exercise and actually can be useful for self-defense in a limited way, try Chen style Taichi. Look up videos of Chen style taiji push-hands competition. Also look up videos of Chen style taiji vs. judo. You'll find that the best practitioners of that style can actually hold their own in grappling competition. But those are the best, mind you. You'll probably never get to that level. Still, it's fairly easy on the back, it's good at keeping the whole body toned, and it gives you a way of moving ("internal mechanics") that might give you an edge later on in your BJJ/MMA practice.
Hope that helps.