I have a Hampton Bay model E81964 56" . I need a receiver and transmitter which includes reversing. What do you suggest.

I found a kit for you which as you said, includes everything!

Here you go.

Hampton Bay Universal Ceiling Fan Remote Control and Receiver Kit (http://www.ceiling-fans-n-more.com/Product/366_universal-ceiling-fan-remote-control-and-receiver-kit.php)

Home Depot has them.