First of all I'm so glad that you didn't listen to the vets and that you gave your bird a chance at life-sometimes we know better than the doctors do, and when we're talking about ending my baby's life I'm going to do everything I can to save him, as long as he's not suffering.
The reasons for his plucking have pretty much all been stated already, and I think the first step for you would to be narrowing down whether or not your bird is actually in physical pain, or whether it is a psychological issue, such as what Wolf said about him being used to plucking even though his actual pain or discomfort is gone. I don't know where your vet stands on trying to diagnose the cause of his plucking (if he wanted to euthanize him he may believe you're letting him suffer, which is ridiculous but it happens). As stated already I would try an aloe Vera spray (make sure it is bird safe) and see if it helps. If it stops him from plucking then you can assume that his wounds are still healing a bit and are itchy (August hasn't been that long ago). They have very thin, delicate, sensitive skin, so after a bad wound it may be quite a while before the areas no longer itch. Also, if he has any pin feathers coming in where he had pulled them out or where the dog pulled them out then that could be causing more discomfort to the areas. Either way the aloe spray should help that particular problem.
If you find it's not an itchy skin problem then I would next rule out whether or not he's still having actual pain, either from nerve damage or from residual bruising and tissue damage. Was he on prescription pain meds from the vet at the time of the incident? You stated that YOU cleaned out his wounds, not the vet, so I'm assuming the vet did very little but stabilize him. If he wasn't given any type of pain medication or antiinflammatory, like Metacam or even an opiate narcotic (which can be given to cockatoos) I would next try giving him the Metacam from the vet, if only to see if it stops his plucking. Again, if it does stop the plucking then you know that he's still having pretty bad physical pain. This may also aide in his leg and wing rehab. If he's no longer in any pain and has no more residual swelling he will not only feel better physically, but he'll be under much less mental stress. I'm not a big proponent of giving my birds or my dogs medications often, but there is a time and place for them, and if your bird was hurt badly enough that the vet wanted to euthanize him, then he must have been very badly hurt, and plucking could be his way of saying "I've had enough of this now daddy, I hurt!".
If all physical interventions fail to stop the plucking then it's fair to assume that he has developed, for lack of a better phrase, "a bad habit" that is bringing him some comfort in a weird way. The mention of an E collar is a very good idea, and one that has had some success. It allows the bird's feathers to grow back in (where there is no follicle damage), gives them a long amount of time without plucking, and hopefully by the time his new feathers grow in he'll have no more physical discomfort and he will have lost the bad habit. The "wing/leg sleeves" are the same idea. The problem with plucking is that they never allow themselves to heal completely, and it's a vicious cycle.
There are many things you can try, and if he's gotten this far then he's a tough bird and he has a family that loves and cares about him, so I believe he can beat this and get back to being himself. It will just take some patience and perseverance.