The pain with running could be a running technique issue.
Have you had anyone look at your running mechanics?
Good to hear you are seeing improvements as you work with the elements in Becoming A Supple Leopard.
As Kelly has noted, “Injury to your central nervous system is a bummer, at every level. Tweak
your spine and you don’t want to move very quickly, much less lift
heavy weights, fight, or sit in a car for any extended amount of time.”
This may be a situation that takes time to get back in order.
Has your physio given you any suggestions on what to do?

Is your thoracic spine tight?
You may need to clean up your t spine position/mechanics.
You may have a downstream impact of an issue at the t spine.

The QL Is NOT a Bone…Even in THE Matt Chan

As kelly has stated in other videos, the key to relief is though giving the damaged tissues slack.  One area that has helped me with lower back pain is smashing my hip flexors.  This is difficult to do but I found a way to do it that makes it a lot easier.  Start by finding a normal sized chair and putting the left foot on the chair, then take your left elbow/forearm and dig it into the crease between the hip and quad, it should hurt.  The mashing technique that works best for me is to try to move the muscles from the inside to the outside or working outwards, starting in the deep crease of the hip and working to the knee.  Then repeat with the right side. If a person is experiencing a moderate to severe amount of lower back pain then one side or both hip flexors should be tender to work on.  The next thing to do is put the left foot back on the chair, and in a half squat try to get the left knee out and past the left shoulder.  Repeat with the right foot/leg/shoulder.    Your back pain should dramatically decrease.