You're asking for trouble, pouring footing concrete into muddy holes. Almost a sure guaranty for uneven settlement (and a crooked swingset).
Wait for drier conditions, then scoop the muck out of the holes and tamp the dirt before pouring. And pick up another bag or two of Quikrete before you start--one 80-lb. bag will yield 0.6 C.F., while a 60-lb. bag yields 0.45 C.F. Based on the dimensions you listed, you'll need almost 1.4 C.F. total.