You are massively overestimating the time dilation on that trip. You need to be getting into the 90%c range before you start getting into decent amounts of time

You are massively overestimating the time dilation on that trip. You need to be getting into the 90%c range before you start getting into decent amounts of time dilation and then you start hitting into the increase in energy required for the same acceleration, as your nuclear power plant or whatever has also slowed down along with you, while you are increasing in effective mass. edit - also, it is Alpha Centauri