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.