You want a patient who's awake, oriented, cooperative, able to protect his airway, able to function without PPV, and possibly easy to reintubate if needed.
First of all, putting somebody on high-dose propofol shoots you in the foot regarding precedex (the latter is a waste of money in this situation). As any other GABA medication, propofol can create delirium and confusion, and it's not your friend if infused at high dose for days. So that would be the first thing to take off or minimize.
Second, what does "maxed out" mean? You need to tell us more about the exact doses.
Third, get an anesthesiology-trained intensivist to help you. You guys sound like amateur hour, no offense. There is a reason anesthesiology residency is three years.
Fourth, in the meanwhile, get your vent settings in order (preferably PSV), and add some fentanyl if the precedex doesn't control bucking. Try to minimize further sedation with propofol (or anything that could disorient the patient), because you have done enough damage already apparently. It may take up to a day or two for that patient to be extubatable, depending on the cocktail of poisons administered. It sounds that you have been giving a bit of this, a bit of that.
Also, use haldol if you need something to treat delirium with (if you're sure it's delirium); stop pussyfooting. It's not like you're putting the patient on it for life. Watch the QTc. And have your attending actually spend meaningful time weaning that patient at bedside.
Don't play with any of these without an attending at bedside.
If you're wondering why this post is not friendly is because I hate bad medicine, especially bad critical care. The patient should have never gotten this far. One doesn't need to be sedated into oblivion just because one has a tube. I had patients watch TV with the tube in, for DAYS. And I'm not even that good. Intubating a patient should be the exception, not the rule, and same goes for heavily sedating an intubated patient.