G.P.
My son is almost 1 and still has that gag reflex too. Sometimes for foods he really doesn't like - peas, and sometimes if I make his food too thick. I would look at the #3s that you are feeding her. My son doesn't like a lot of those, and especially things that are tart (the apricots seem to be pretty tart). The textures of those are weird too, I find that some of the chunks are pretty hard, and the rest watery.
I typically make my son's food and have just been going thicker and thicker, and leave in a few soft chunks. The yams work really good to get the thickness, but the first few days he will gag. I might thin it out a little, and then he will get past it and is okay. Also, I notice that he is less picky at daycare and doesn't gag nearly as much (except with peas!). If I am having trouble with a certain food at home, I send it to daycare with no issues.
To make the food, I steam the fruits and veggies and sometimes give these to him as finger foods. They are a bit mushy, and messy, but he seems less likely to gag on these too.
There are also some gerber graduate freeze-dried fruits and puffs, and some yogurt melts. Yogurt might be a good addition for her too.
Good luck, and let me know if you find some good ideas for the next steps.