Even with only two leadscrew, the bed leveling works well. I don't bother with the mesh bed compensation anymore. Just stick the following codes in the start gcode of the slicer and the first layer come out almost perfect every time.
G28 ; home all
G30 P0 X0 Y240 Z-99999 ; probe near left leadscrew
G30 P1 X540 Y240 Z-99999 S2 ; probe near right leadscrew and calibrate 2 motors
G28 Z ; home Z
Now I am just waiting for the delivery of the third lead screw to make it even better.