Oh, I feel your pain! My son was the same way! While he didn't go as long as your daughter with the texture aversion, it did last a long time. He couldn't even have birthday cake at his 1st birthday party! We just had to go with it for the most part. I would try things here & there, some days were good, others we were covered in throw-up. He was on Stage 2 forever, but finally moved up so easy Stage 3's and moved up again to chunkier finally. He teethed real late, cut his first at 11 months (he's almost 21 months old and only has 6 teeth) and was a late walker, too. My daycare actually tried to force me to let them give him solids, but a doctor's note kept that at bay. I think we were finally able to move on to solids for good around 15 months.
In the quest for solids, in these cases, it's about time & patience. He'll still gag on things every once in a while & my head whips around to make sure he's okay. After going through all that for months, old habits die hard. If there's anything more I can do for you, please feel free to contact me! Even if I just listen. Trust me, I know how hard & frustrating it can all be.