This is sideways and will probably come across as useless and irritiating, especially if you have suffered for years with a back and have heard it all before. I know how you feel.
I go through periods during the year when I have to sit all day and, time was, I invariably got a bad back during those weeks/months; one consequence being a rotten kip generally and aching on a sleeping mat. This is on top of the generally battered and torn condition of my corpse. One can't deny that a good, light inflatable mat helps. I like the Thermarest Neo Air, even if it is a bit noisy.
But, over time I have found that targeted exercise works ... For me, 30 mins on the elliptical machine in the gym, dead lifts, a variety of air squats and weighted squats (single and double leg), pliés, glute bridges and other related exercises that tighten your bum and core seem to nail the problem, along with stretches for hip flexors, calves. And, should you ever get a chance to have someone practice myofascial release massage on you, do be sure and take the opportunity
Fact is that hiking with a bag on uneven terrain is unusual exercise, even if it doesn't appear arduous at the time, and our bodies (tuned to bowling along on even pavement) can expect to hurt afterwards. I guess my point is that one needs to train a bit as we approach our golden decrepitude. (Personally, I get quite anxious around November that I haven't done anything to toughen up my legs. Skiing and snowshoeing - there's nothing else to do here - can be fierce on you, leading not just to crashes but torn or sprained ligaments just through the exercise itself, and it isn't as if these are pursuits that provide in themselves sufficient exercise to strengthen in the areas you need it. Backpacking is the same)
The exercises I mention all work to straighten out my gait too .. which gives my knees and ankles less of a pummelling and leaves them less sore. Misalignments from the leg joints have an effect on your back, and anything you can do to regularize your gait will help.
Seriously, look at Pacerpole: not just for their hiking poles but also information on walking mechanics, the back and shoulder girdle and techniques of walking and posture to minimize irregularity. Contact them. Heather Rhodes is kind and helpful people.
You might also look at packs which arrange the weight around your hips ... Kifaru used to make something called the TailGunner, and do a Hellcat now. They are not that cheap, but you'll get the idea by looking at them ... also packing so that the weightier stuff is low in the bag helps so that your back muscles (esp the Erector Spinae etc) aren't continually struggling to balance the weight higher up; which tires the body, making it take the burden inefficiently elsewhere and which leads to pain. It really is worth doing a little research to find out which muscles attach to where and the kind and location of pain they produce if they are not doing their job. It helps, if nothing else, by getting you to think about gait, posture and mechanics.
Of course, yoga does help. Work your way into it. Find a beginners class if you haven't done it before, and don't get put off if your first, second or even third instructor is a bit of an idiot. Persevere and find another. There are plenty of good ones out there. You don't have to go bounding around twanging your underluggage to get the benefits and it will help you with your horizontal life.
As I said, none of this is of much use if your bad back is coming from mechanical degeneration in bones, tendons, discs etc. and can be pretty irritating to hear about .. .again