Chicken – Smoked a chicken and the skin came out like boot leather

I suspect you may have created a poor-man's slow-cooking environment in there. You had meat, and liquid, and a median temperature of around 200° F, and you probably also got the bird close to "done" during the first broil, before you even left the house. This is obviously easier to do when the meat is covered (was it in a covered roasting pan?) due to the steam, but the oven does provide some insulation to begin with.

Technically when slow-cooking you should theoretically be able to speed up the process by quickly bringing the meat up to just below doneness/moisture-loss temperature (130° F) and then switching to a moisture-preserving slow-cook method like braising. I think that's what you accidentally did, but it's hard to say for because nobody was there for an hour and it sounds like you didn't check the temperature before the second round in the oven.

My guess is that the second roast at 400° F was probably unnecessary, and that the bird was already done, having been cooked in a very slow roast.

I'm pretty sure it wasn't the basting that helped. It seems to be regarded as a myth these days that basting keeps the meat moist, because the baste really doesn't penetrate the skin (and it's not the skin you're worried about). Basting is done to add flavour, not preserve moisture.

The recipe itself also doesn't strike me as anything special in terms of keeping the bird moist, aside from having a relatively short cooking time (as with any grilling/broiling) and letting the meat rest afterward, neither of which really apply in your case. It was probably the slow heat that did it.

Chewy means undercooked. Most of your standard "barbecue cuts" of meat contain a lot of connective tissue. This must be rendered to achieve tenderness. This goes for brisket, pork butt, and ribs, to name a few. If you are using the words "chewy" or "tough" to describe the texture of your meat, in nearly all cases it has not been cooked enough. Your time/temperature pretty much confirms it.

The best thing you can do is deemphasize time and temperature as your measure of "done." Rather, use a skewer to probe your meat when you think you are getting close. It should slide in and out of the brisket with VERY little resistance. Some people like to wrap in foil a few hours in. This will finish the brisket faster, as you will mitigate the evaporative cooling effect that causes your cooking process to stall. Plus, you can add some liquids and spices to the foil, which adds to the flavor profile of your meat. This is better known as the "Texas Crutch," and there is no shame in using it. Plenty of competitions have been won employing these tactics.

Brisket is a little intimidating because of the small window between "too chewy" and "dry and falling apart." But you should probably err more on the side of the latter, as that can be more easily compensated. The real takeaway here is have patience, and look to the meat itself for clues as to whether or not it is done, rather than using a timer and thermometer.