RE: Barbell Step-up
Good exercise to incorporate as if the step is high enough you're almost doing a 1-legged squat to get yurself to the top of the step/bench, providing you don't push too hard with the trailing leg.
Easier to keep upright doing these than squats if that's the cause of your LBP.
Have you looked at front squats as a substitute for back squats. I too find I bend more at the hips than the knees and take too much of the weight on my lower back. Doing front squats means I have to maintain a more upright position otherwise the bar simply slips off.
Some kind of squatting would be useful in a routine.