Dereck, have you thought about dumbell lunges as an alternative to squats? They would not only work the legs more completely than extensions, but also address your interest in core activation, as well as traps and grip work. Just a thought.
Weight training is a little adaptive at the moment as I am recovering from a lower back injury, so predominantly high intensity machine work, geared for muscle growth- just for fun really
Your back is it a disc problem? Just asking. I have had to adapt my training to take in to account a lower back injury substained some time ago.
Everything is back to normal other than I wont squat heavy or deadlift at all. I hear of power lifters who go back to heavy training after a back injury. I presume there must be a method of making sure a disc is healed or not?.
Instead I do high rep free hyperextentions, ,normal/ heavy weights for leg press and leg extention/ curls. Squats are hack squats done quite light but high reps. Running and practicing judo/ mma aren't to much of a problem.