Hi -
Here in Lawrence, MA we have a traditional sandwich called a "Chicken Barbecue". It doesn't have BBQ sauce, but, rather, mayonnaise. We prepare the chicken as you do, but we do not thicken the little bit of broth we use to keep the chicken moist. (Though, I think that sounds like a great idea.) We put the shredded chicken in a saucepan and keep it warm on the stove (or crockpot). When ready to serve, we take some good quality rolls (most probably from Tripoli's bakery!), butter the outside of the rolls lightly, spread mayonnaise on the inside of each piece, place the chicken in the middle, and grill them on both sides, pressing down to slightly compact the roll until both sides are golden. The grilling keeps the bun from falling apart as you eat it due to the juicy filling. The other sandwich we have is a "chop suey" sandwich where we do thicken the ingredients before putting it in a roll. (It's sort of like a Chinese sloppy Joe!) Hope this helps with your quest!