I had the same problem with my son last month (he was 11 months). He gagged on the 3rd foods. What ended up working was this...
I started with oatmeal cooked til it looks like the kind served in restaraunts and mixed it with his jarred baby fruits. I added less and less fruit each time.
Next I gave him homemade split pea soup.
Then, I started giving him lumpy foods along with pureed foods. For example, I gave him finely chopped chicken and diced cooked carrots along with pureed peas (the baby food in a jar). I would give him a bite of carrots, then meat, then peas. The peas helped the meat to go down since it tended to get stuck in his mouth as he gummed/chewed it.
It has only been a month, and now he eats what we eat. Last night he had finely chopped meatloaf, mashed potatoes (a little runnier than ours) and whole cooked peas.
I found the wetter meats were easier on him. Deli turkey and chopped ham were good, for instance, because they slide in the mouth easier, not getting stuck.
Some other suggestions...
canned carrots and green beans (cut up)
cooked peas
canned peaches (cut up)
banana pieces
beef (ground or steak like) that has been cooked in soups
rotisserie style chicken is very "wet" and easy to swallow
beans (black, red, northern)
fresh or thawed SMALL blueberries
rice, spaghetti noodles
Good Luck. He'll be ready for that birthday cake soon!