Cream cheese is meant to work well to keep lean meat patties moist, and I imagine that would taste good without adding to the liquid content and making them sloppy like extra egg yolk or olive oil might.

For next time, I think thighs would be better, but you could also try not cooking the chicken breast first - ie, use either minced or small cubes of raw chicken made into fingers. Once-cooked chicken breast can be fine. Twice-cooked is bound to be dry.