It is the toxins in the waste produced by the bacteria that are responsible for food-borne illness. Heat will kill the bacteria, but will not neutralize the toxin.
Yes and no. It is true that the waste toxins are what create the symptoms, but regarding food-borne illness it depends on the bacteria. Botulism, for example, is caused as you described, by eating food contaminated by the toxin created by the bacteria, even if all the bacteria are dead.
But salmonella, the most common poultry contaminant, does not create food-borne illness that way. It creates it via infection, where you consume a large enough dose of the bacteria that some survive the acidic stomach and enter the small intestine and multiply. They then need an incubation period of 6 to 72 hours before they begin releasing toxins and make you sick, which typically takes 12 to 36 hours.
But having a salmonella-tainted bird in the TDZ for a longer period of time while slowly cooking as we're describing will not make you sick, as long as you cook to the proper final temp. The amount of time we're talking about does not give them the opportunity to incubate and produce sufficient toxin; you must get infected by live bacteria.
On the other hand, the other subject mentioned of stuffing the bird is a different story. The risk with that is salmonella-containing juices from the bird can drip down into the stuffing, and then though the bird is cooked to a safe temperature, the stuffing in the center may not reach the same temp and the salmonella survive, creating an infection when consumed. Cooking your stuffing separately is the safe practice.
Of course, not all birds are contaminated. You could undercook and be just fine, if your bird is clean. But there's no way to tell in advance, outside of a lab test. The concept behind safe food handling practices is to treat all food as if it were contaminated, so in case you get a piece that actually is, you'll be safe.