For the formula you can try to find pigeon pellet food. It a complete food for adult pigeons and looks like granules. You can grind them up in a food processor or anything of that sort, and if you have that wide neck syringe it will go trough easily for feeding. This is just for instead of formula. If not you can sift the grinded pellets 2 times and use that. As for seeds in his bowl add more larger seeds, use defrosted peas as Vicious explained, and even these pigeon granules. I've observed pigeons learn easier with larger seeds and especially granules. In first he will pick the large seed and his head will go all crazy and he will toss the seed over his back. But once he overcomes this and finally manage to get the food to the back of the throat, larger things are easier for him to push back and swallow. When I say larger things I mean like corn kernels, peas, and pigeon granules, not something he can choke on. If he eats pigeon granules just be careful that he also needs to drink water and they expand. So give in the begging just 5-6 so he practices, but not as main food untill he eats and drinks on his own. Also he will be more motivated to eat if he has larger seed because a few larger seeds eaten will provide some satiation, as budgie seed has very little energy value to pigeons. Corn, especially red one if you can find it, sunflower seeds, large grain, peas and granules would be better to practice.
Finally to know if he is really eating on his own look at the poop. Pigeon digests everything in 2 hours, so you should see, after feeding, that he has cleared out of the formula - pale feces, and if he is managing to eat, the feces will be still full - meaning you can see its coils, it is not just a litle bit of colored mucus, or small pieces of it, but it will change color to deep green or brown, depending on what he is eating.