Is there a link between poor posture and rounded shoulders and SI Joint dysfunction?

I have persistent pain in my right SI Joint, which radiates out in to my buttocks, groin, hips, lower back. It even clicks when I stand up or push my hips forward. If I do any sitting, bending over or jogging my lower back seizes up.

An X-Ray shows inflammation in the right SIJ. The Rheumatologist says that following various blood tests I have no degenerative diseases such as AS or Arthritis. Two Neuro-spine surgeons (one I saw privately) says that of my CT scan of lower spine and pelvis they can see no disc damage or degeneration, nerve damage or anything of concern.

My physio says she thinks the tight muscles (glutes, piriformis, hip flexors, erector spinae) are a response to the SIJ dysfunction, as the joint is painful to press. I have now seen two different Chiropractors who have also diagnosed that the right SIJ is getting stuck, and they both think the muscle pain is just standard secondary pain to such a dysfunction. They are though unsure as to why it keeps getting stuck.

I did read that poor posture and in particular rounded shoulders can somehow affect the SIJ, as it causes the upper-mid back muscles to stretch and some of these muscles (possibly lats) may be connected to the iliac crest! As I do have quite rounded forward head from years of heavy bench and an unbalances workout routine, plus sitting slumped at a desk all day, I am starting wonder if this may be linked. Could someone please tell me if the posture and rounded shoulders could causes SIJ dysfunction, and what muscles in my back if any could be responsible?