In a small bowl, stir together the honey mustard and pineapple preserves. Divide the mixture evenly between 4 of the tortillas. Spread evenly to within 1 inch of the edges. Distribute the Swiss cheese, chicken, bacon evenly over the pineapple mixture; top with remaining tortillas to make quesadillas.
Preheat the oven to 250 degrees F (120 degrees C).
Heat a large skillet over medium heat. Melt a small amount of the butter in the skillet, tilting the pan to cover the surface with butter. Place one of the quesadillas into the skillet, and fry on each side until lightly browned and the cheese has melted, about 1 1/2 minutes per side. Keep cooked quesadillas in a warm oven while you fry the remaining.
To serve, cut each quesadilla into 6 wedges and arrange on a platter with pineapple tidbits in the center.