The term 360° servo usually means a servo that has had its internal potentiometer disconnected so it is no longer a servo but a gear motor that can have its speed and direction controlled by a servo signal. They are also called continuous servos. Since the feedback mechanism is disconnected they cannot have their position controlled. You might get close by timing, but if you change the load that timing will no longer work.
I repeat, continuous servos are NOT servos. Their position can not be controlled, only direction and speed.
Yes that's about as good as you can expect. In those 'ex-servos' using write() with different values has nothing to do with position it just affects the rotation speed but it's not really calibrated in any way.