How's the stalk health of your corn? Will it stand a while?
It may be wise to be patient for a while. Mudding up the field won't make farming next year any easier. You can feel the effects of compaction for a long time.
My corn experience is from WI and IL, a lot different than your climate. It can stand quite a while up here in the fall (or winter!) and isn't as vulnerable as, say, wheat. However, we don't have your heat or humidity causing grain quality issues, or stalk health issues. That same heat should help dry out your fields sooner, too.
Mud here in November will freeze up faster than dry out.
Curious- How wet is the corn grain?