Cookie Encyrption Question - I'm confused

As you say you are only interested in the BIGIP cookie: encrypt it in the cookie profile instead of http. It is easier to maintain there, and you don't risk interfering with an applications cookies.

If you only want to encrypt the BIGIP cookie, but use the http profile to do it, it seems you need to take the name of your cookie and add that to the http profile as well.

Choose a randomly generated key/passphrase for it (a long one) and store it in your password vault. You never know what you might need in future troubleshooting scenarios.