Too funny, I just had a conversation with my 13 year old (who refused to hold her bottle, cup or feed herself for two years) about lunch. She wanted beenie wenies, and "needed" me to go open the can and cut up the wennies...which she can do with her eyes shut. Sometimes it is just personality.
If she gags on something, feed her what she likes. If chopped table food is working, then chop more table food. We used a slap chop for our youngest child, she ate everything we did, never liked baby food, but as soon as she heard the slap chop at work, she came crawling...then running! So find stuff she likes, and if she can eat chopped stuff, you probably don't have a feeding issue!
M.