It wouldn't need to be halfway. At 3gs acceleration, it would take about 115 days to accelerate up to the speed of light. You'd then travel ballistically for the majority of the journey before having to decelerate for another 115 days.

Given the total journey would be ~40,000 days the 230 days of acceleration probably isn't going to impact things too much. Even if you brought it back to 1g acceleration, it's still only around 700days out of 40,000.