Booking flights without the games

Marginally. The reliable part is that prices rise close to departure and dip on midweek flights, both of which you can exploit without a tool. Set a price alert, book when it is acceptable, and stop watching, because the regret costs more than the difference.

Shift the light schedule, not the sleep schedule: get bright light in the morning at the destination and avoid it in the evening. Melatonin helps at small doses taken early relative to the new night; large doses mostly make you drowsy at the wrong time.