The optimum solution is a recumbent bike - by going feet-first, you can reduce your frontal area by more than 50%. With a much smaller frontal area and a much lower center of gravity, a tail fairing becomes a practical proposition.
Fully enclosed recumbents can achieve phenomenal results in the right conditions (Sam Whittingham's 91km hour record, Andy Wilkinson's 41 hour LEJoG), but they immediately become a handicap with any sort of gradient because of the ~20kg weight penalty and they're unbearably hot.