It would be great to get some advice or prior experience from people who have overcome a similar type of injury.
My GF, beginning of last year, had a bulging L5 disc from kettlebell swings, which subsequently turned into sciatica. She has now got rid of the sciatica and the bulging disc has fixed itself, but suffers from almost the exact pain you are describing.
She has had so much therapy - you name it and she has tried/doing it -she last week went to a back specialist, who is supposed to be one of the best in Australia, he told her that because she is hyper mobile, the pain is caused by over-releasing the muscle around the sacrum- from all the therapy she gets - and basically everytime that she releases these muscles that short term pain relief is had but the muscles seize back up to stabilise the area, causing the tightness and pain. Therefore, he told her that she needs to strengthen her pelvic floor, core and generally get stronger. Although she agrees, in principal, she thinks there is something more to the clicking/popping in her SIJ joint.
What type of exercises did you find helped you? And has the pain subsided significantly? or still just as bad?