when referring to a lazy "S" configuration of the flyline on both the back and forward stroke. In fact, before the flyline straightens out on the backcast, it does look like a lazy "S." You are correct on the forward cast configuration appearing to be a sideways "u."
An excellent aid to depict flyline form and to commit to muscle memory is your "boa" or the Fly-O sold by Joan Wulff.
This is a welcome addition to the forum and not readily available elsewhere.
Juro, good Job!