I would also second asking your pedi, since s/he is familiar with your kids' personalized needs.
We were given the go-ahead at 12 mo. actual (31 weeker), but I had enough BM in my freezer to get us to his adjusted b-day. So we just did a slow wean over the course of about a month around the birthday--we intended it to take about 2 weeks, but I underestimated just how much BM was actually in the freezer and didn't want to waste any. He was ready to wean at his actual b-day, I think, just had the resources to wait.
We also made a big point to offer different food textures at that point even though he wasn't wild about non-grain, non-puree textures. OT helped with some of his feeding issues and we fixed them in a few weeks to the point where he's eating with age-appropriate pickiness but is able to eat the food. If you haven't already looked into EI, I'd suggest calling for a consultation. GL!