Firstly, every time you work with your horse from the moment you halter him, to the moment you turn him out is a training session. They're 1200lbs and you definitely want to make sure that they listen to you and are not causing you to fall down, but also you want to learn to communicate with your horse so he respects you. It sounds like your horse needs a lesson on ground manners (and they all do sometimes) but think of your training sessions with your paint like this: when you bring your horse in work on whatever it is that they're showing they need to work on that day -in your case, leading (my mare yesterday, she is broke and leads well, but i noticed her flinching a bit at the stirrup before i mounted, so spent some time sacking her out again so get her used to it).
As far as leading goes, I have found that lead training works really well in a bridle, I have bridled my horse in the field to bring her and as you have much more control, you can pop them up if they lean down, turn them, or back them up. I would go into a field, and walk him back and forth over grass without letting him stop and eat. when you're done give him praise and some pets then take him inside and begin the riding session. At the end, Iw ould also do that and when he stops trying to eat, turn him out with praise.