I think you will experience problems with the linear Hall effect device. Your magnet structure even possibly the feild of the voice coil itself may alter what you are sensing. In the old days of big computer hard drives, voice coil head possitioners were used. Some of them were really massive with magnet structures weighing upwards of 100 lbs and voice coil lengths of 6 inches. The position of them was generally sensed using an LVDT. It was commonly attached to the voice coil through a hole in the center of the magnet center pole. Since they operate at up to 50 Khz drive and sense frequency they were unaffected by the voice coil drive.
I had a small LVDT and it's indicator once, made by Swiss Precision and it's readout was in mils (thousandths of an inch) with 2 places to the right of the decimal! 0.00001 inches !