R.,
I think it is fine if he is still having jarred foods, only 9 mos old and each baby developes different. Each of my kids were different went it came to moving on to table foods and chunkier food. Maybe wait until next month and add some rice cereal to the puree foods a little at a time. Sometimes they will just move past the 3rd stage food strait to table food.
Did he spit up alot as a baby? might still have an easy gag reflex. My dd 7yo still has an easy gag reflex if she eat something that she doesn't like the feel of she will gag.
I think it is great that you are giving the finger food peas and carrots are great for learning plus the peas taste sweet, and added bonus when the are learning to eat table foods. Maybe try a very steamed yam or boiled spinach finely chopped and add that to pureed foods or mix some formula or breastmilk w/ it to smooth it out. Just be creative, let him have fun with it. We all do better at things when we think it is fun :)
I know it get trying on your nerves when things don't go as smooth as you would like, or think it should happen. I have 4 very different children and wow I've got lots of grey hair to tell the stories LOL.
Good luck!!
L.