Buy birds and roast 'em. Let them half cool on the stovetop and picking them apart is super easy. (To shred a cooked chicken breast just roll it between your hands.) 2-4 birds at a time depending how I'm eating. Freezes ok in zip bags if required. Insert into any recipe. Simmer the bones overnight for stock (soups, gravy, sometimes I just drink a cup of broth), fridge and scrape the fat off the top. Buying just breasts is a joke.
If you have a pet, it will come to know this routine real quick. Dog quality meat/ biscuts/ broth is a big hit. Careful about bones, of course.
It probably burned to your grill due to sugar or HFCS in the bbq sauce. Sugar burns quick & hard. I'm no bbq expert but molasses is probably the traditional choice due to its pre-burnt/ resistant nature from being the sludge nearest the heat. I never put sugar in bbq meat marinades. Finishing glazes yes.