I'd get your pelvic alignment checked. If your hamstrings are tight you may have decreased curvature in your lower back. Causing it to get sore. The stretching you are doing may not be enough, are your hamstrings tight? I am just a bit skeptical about the sneakers. When I run with my "old sneakers" it bothers my knees not my back.
I have extremely tight quads, I have for years from martial arts. That also never has bothered my back.
Fitday start date 12/9/12
Fitday start weight 190
Highest weight Jan 2009 218
Lowest weight Aug 2009 175
Goal 160: ACHIEVED Aug 25/13 (now to figure out how to stay here)
If you do what you’ve always done, you’ll get what you’ve always gotten. –Tony Robbins