We have a friend who used to be a very keen cyclist, mostly road. It was his main hobby and he covered thousands of miles a year. He developed lower back pain which eventually resulted in a chronic condition that led to him being off work for almost a year, at its worst he could do nothing more than lie flat on the floor all day. When he was fit enough to go back to work he had to leave the company he'd been with for something like thirty years and find a job that required less driving, as he could only sit in a car for a limited time.
He's back cycling, even on the road bike sometimes, and has taken up hill walking to keep active. It's taken years though, and you could often see the pain in face, even years later. My point is that whatever you do about the back pain, don't ignore it.
I have suffered from back pain in the past but over the years I have found ways to eliminate it. It was very simple. What I found was that all it took was one or two regular bad posture situations to cause prolonged back pain. I my case there was something I did at work, the chairs we had at home, that kind of thing. We changed the chairs and I found another way to perform the task at work.
If you find something that is causing you back pain, remove it. The results of not taking action can be very serious. Perhaps there are other situations in your life that are contributing to your pain and resolving those may be enough to allow you to continue using this bike without issues.
I sit on chairs in a completely different way to the way I did when I was younger. It seemed odd at first but I do it without thinking about it now. I know exactly what things will give me back pain, totally subconsciously I avoid them and now I never get a sore back.
I wish you all the best with getting this sorted out. If you do your home work and look carefully at your routine I'm sure you can sort it out :0)