Every once In awhile I get pain in the right SI joint while lying on my back. I clench my glutEs and some bones pop (not sure which but probably sacrum and iliac crest) and the pain instantly goes away
One thing that might help a great deal for this is finding a VERY good massage therapist. If he/she can loosen up the gluteus medius and some of the things that might be pulling on things it might help a great deal
Also PTs and MDs vary greatly in quality so it may be worth it to travel to find the right one
Another thing that might really help are hip flexor/lunge stretches holding for 3mins on each side. This, combined with regularly scheduled deep tissue massages, really helped loosen up my back and probably improve my pelvic tilt. The anatomy in this area is complicated and unfortunately most MDs only see a patient for a 2min appointment and just send you off with Rx for pain and that's it so i learned from my own injury struggles that for runners, really the only useful healthcare professionals in general are massage therapists, PTs who are runners themselves, a few MDs who are runners themselves and possibly yoga sessions because they can really stretch the hips out.
One place in particular that was really helpful for me was the UVA speed lab at Univ. of Virginia in Charlottesville VA. I saw jay Dicharry, Eric MagruM and dr Robert Wilder and that team was extremely helpful along with massage therapist Ernie Kidd.