If three wraps don't work...
... use four. On big racing boats with winches the size of Lewmar 72s it's not uncommon to put five wraps on the primary winches. My primaries are 48s, and although I can usually get by with three wraps on my jib sheets, thanks to being fraction rigged, I don't hesitate to add a fourth wrap before final trimming if I'm beating to weather in a good blow. Don't start the tack with four wraps, however, because your chances of getting an over-ride at that point go up exponentially.