there is ZERO need to push a dog that is already fear avoiding to the point it will bite just to see if it will engage and "build confidence" It's disaster waiting to happen.
Dogs with confidence are taught bitework. Dogs that are fearful, and from your description I don't have much doubt your dog has weak nerves and is very fearful, should absolutely NOT be taught to bite.
Think about it. IF a dog is scared, they bark to get you to move away and when you don't, they try to get away. Ie, your dog backing off scared and shaking. Then some "brilliant" trainer decides to push further with a sleeve to get them to bite. You didn't build confidence, he's teaching your dog that when it feels scared it can turn off whatever is scaring it by biting whereas now your dog puts up a front then hides when it's too much. Much safer for people and the dog.
Some dogs need to be managed, they need to managed their entire lives and all the expensive trainers in the world aren't going to give strength to nerves that aren't there. You can socialize, make comfortable in some situations, but YOU always have to be aware of minor changes that will immediately take your dog out of its comfort zone.
Any dog that is lunging and jumping and has unwarranted aggression to non threatening people is a dog that needs to be managed and socialized heavily with constant supervision from their owners. Absolutely NOT a dog you push to the point of biting so it can learn to turn off pressure or deal with stressful situations by biting. Great deal huh? These trainers aren't near as good as they've led you to believe. Save your money.