I'm no expert and I've received a lot of help here, but I have to tell you I've been doing poultry at 350 to 375 and it's coming out absolutely wonderful. And in my opinion (because I tried early on) 250 is not hot enough, ESPECIALLY for a 20# bird. I'd cut it at LEAST in half and consider doing more to make the pieces smaller.
10 pound turkeys seem scarce as hens teeth, but 12 to 14 I can usually find. I have a turkey in the smoker right now (at 375 for the first hour) and it's 14.75 pounds. I won't do anything bigger than that whole. I prefer a 12 pounder, but none were available when I was shoping for a turkey.
Again, I'm not as experienced as some on here, but I've gotten pretty good at cooking chickens and turkeys and I've learned a lot here.
#1 They don't NEED low and slow. In fact they seem to come out better when cooked faster. High temp at the beginning, roll the smoke, after an hour cut temp back to 325-350.
I know a chef that runs turkeys at 400 to 450 ALL the time. He has to watch he doesn't burn the skin, but they are as moist and perfect as anything I've ever had. Every single time. They aren't smoked though :)
I'd be kinda scared to do a 20# bird at 250. I was taught that poultry should never be cooked at a temperature below 325 for safety reasons. Not sure if that's in keeping with present-day thinking, but it has kept me out of trouble for 50 years (I started cooking for others when I was 10 ... hehehe)