Regardless of whether it feels right to you, that 4x boost in belt frame is correct. It's just how the maths of SR works out. As I have tried to show, one can tackle it from multiple pov, in either lab or belt frame, and as long as SR is consistently applied, the end result always agrees. SR stands for special relativity. Relative to the belt frame, the lab frame is undergoing a vertical acceleration 4x that measured by a stationary accelerometer in the lab frame. As the maths shows. This is not Galilean relativity. It's not Newtonian physics. But SR has been experimentally and observationally confirmed to very high precision in countless situations. So we accept it as true.