I will agree that there must be a way to cook a Turducken without drying it out. I will also agree that the way it is constructed, getting the chicken in the middle cooked without drying out the turkey on the outside would be a difficult task. After all, just roasting a stuffed turkey to the point where the stuffing is cooked to an adequate temperature and the turkey is still tender and juicy is an almost impossible juggling act. I never stuff my turkeys; I put my "stuffing" in a glass baking dish and put it in the oven when the turkey comes out and is resting.
I will also admit I have never attempted to roast a Turducken, nor do I think I would ever want to. I agree with the earlier post that says the novelty mostly outweighs the actual quality of the meal. And as I said, I have never cooked one, but I know a bit about roasting birds. However, if someone were to put a gun to my head, and insist I cook a perfect Turducken or else, I would preheat my oven to 250 degrees (for about an hour) stick my thermometer's probe all the way into the chicken portion, put the Turducken in the oven, and then wait until the thermometer read about 155 degrees. I would then crank the oven to about 450 to crisp the outside of it, and pull it out when the thermometer read 165 degrees. I would then let it rest, and finish up my side dishes.
At 250 degrees, this would take a lot longer than roasting a normal turkey, but I think the results would be superior. In my experience, injecting and basting are largely useless. Even if you inject poultry stock or real butter, the results are most often less than spectacular, and basting pretty much ensures a soggy skin and vastly increases the cooking time without adding any juiciness to the meat.
Another option I might consider is to deep fry it in peanut oil. At the proper temperature, the oil will work to hold the moisture in. However, I would not be sanguine regarding it holding together while doing so. I would have to make sure it was properly trussed first.
Of course this is all theoretical. I would dearly love to hear from someone who has experience cooking one. One that turned out well, that is. :)