Myself, my SI pain is only on one side when sitting. There's lumbar pain too, but not because of sitting. To accommodate my sitting, I had to make for myself a soft brace for my left side bottom. It was a rolled up, and then a do-it-myself duct taped thick kneeling pad that construction workers use for hard gravelly surfaces. It was maybe 18" by 2 ft. I happened to have one when the need arose. I put it under my right side on chairs or whatever, so that the left bohunkus didn't have to touch the chair. it takes some getting used to. It also wrecks your posture, but I couldn't sit unless I used it (for years). A PT had suggested a rolled up thick towel, which wasn't quite enough. So, then, I had to get used to carrying a bag (shopping bags work) if going to doctors etc. For some reason, I could sit in the usual public buses, in the middle of two hard seats, but not the sort soft seats the shorter ones usually used for ADA transport or for seniors.

Much later on, when I had a few bucks extra I discovered special sitting (and sleeping) pads that were composed of pillows of large air pockets. I believe they are called Roho cushions and are often called wheel chair cushions. Perhaps a less expensive foam wheel chair cushion would also work for you? Also, I got a recliner that allowed me to sit with my body weight further back, off my SI joints. For years I had to sleep only on my right side, or on my front, or in that recliner. It takes time to find all the workable solutions for yourself. Good luck.