Agree with the previous posters...
To improve your results, you will need to borrow ideas from the disk solution:
1. Get the magnet out from the central axis of rotation (the further the better)
2. Get the sensor closer to the magnet's path (the closer the better)
What you want to achieve is a high rate of change of magnetic flux that is tied as closely as possible to an exact point of the shaft's rotation. You do this by increasing the speed of the magnetic field going past the sensor, by the magnetic field being localised (using a magnet that is physically small compared to the path it traverses) and by the sensor being close to the magnet as it passes.
What I would be tempted to do (if physically possible) is to fit the magnet at the end of an arm and affix the arm to the rotating shaft. If you could get the magnet's path out to a circle of 2" radius, you will find things vastly improved. More than that would be better, but less than that could still offer improvement. Even with the current arrangement, putting the magnet on a very short arm so that is just misses the sensor housing would make a useful difference. (If you used hot melt glue to mount the magnet - just heat it up until it softens and then push the magnet off centre, so that it almost touches the sensor housing as it rotates.)
Oh - and ALL of these suggestions will give better results by getting the sensor closer to the magnet's path.
PS. Forget about a reed switch. That would be adding another level of mechanical uncertainty. The Hall effect device is the correct choice here.