When I had sciatica I went to the chiropractor as the quack could only quack platitudes but give her her due she spent 30 minutes asking the questions and 30 mins manipulating. So we established that doing a somersault from a motorbike buried in a car's back wing and landing on my back in my youth was the genesis of the misplaced disk pinching the nerve that put the pain elsewhere.
Obvious once you are forced to survey the history.
I was lucky with the motorbike/car and lucky with her, she spent about 5 sessions and I never got sciatica since (14 years now).
As an engineer I was more interested in her technique and there is no doubt she shifted a vertabra.
If the physio is not moving the offending disk then the nerve will stay trapped. Chiropractors don't come cheap & mine was recommended by a trusted friend but it did the trick.
I know you don't want to hear this but my hip problems (more recent) changed for the better when I gave-up badminton and upped my ceilidh dancing. It is all about loading and stress. Running may not stress the joints as much as badminton but I bet it has a higher accumulated loading in the balls & sockets.