Moving the saddle forward is the last thing I would do, that pitches your weight even more forward and will make matters worse. Try a entire ride with your hands on the hoods as an experiment, allowing your weight to be more balanced over the saddle and see if that helps. I suspect it will, and if so and you still insist on those areo bars shorten that stem. Lower back pain is my nemesis as well, and even with dialed in fit I sit up in the saddle and stretch out every 15 miles or so, do core work on non-riding days, and try to remember to spin not mash. Good Luck!