As another comment suggests, there are many muscles acting across the pelvis and trunk that might be contributing. A physical therapist will either correctly identify what specific areas you should focus on, or (more likely) make sure that you work them all.

I've had several acute lumbar disc incidents leading to up to 6 months of sustained sciatica. By the end of that time, my hamstrings were indeed extremely tight, from inactivity and sitting.

This is correct. Even though intuitively it might seem unlikely that hamstrings have anything to do with lower back pain, but they really are linked. There are also other stretches and exercises which help.

For similar "pulling" reasons, make sure your feet reach the ground (or a footrest) - you don't want them dangling in the air.

I would disagree with respect to hamstrings. Hip mobility and glute strengthening should be your focus.