Put one chicken breast in a gallon zip-top bag and pound it until the entire breast is uniform in thickness, then move to a platter or rimmed sheet pan. Repeat with the remaining chicken breasts.
Season both sides of each chicken breast with the BBQ seasoning, cover and refrigerate at least an hour.
Combine melted butter, pineapple juice from canned pineapple slices, mustard, honey, molasses, Worcestershire sauce, and chili powder in a medium mixing bowl and whisk until smooth, then set aside.
Grill one side of each chicken breast and each pineapple ring over direct heat until they are seared and have nice grill marks, about 2 minutes.
Flip each chicken breast and ring, brush with the sauce, and cook another two minutes.
Move the chicken to the indirect part of the grill and brush the top of each with the sauce.
Top each breast with two slices of ham and drizzle the ham with the sauce.
Put a slice of cheese then a pineapple ring on each breast and drizzle again with the sauce.
Continue cooking with the grill lid down until the internal temperature reaches 160 degrees F (about 10 minutes).