Linearizing hall effect sensors outputs
Please check again application note!
in this way the output overlap is very important! i thinks you must install the sensor closer than now !
please see this picture from application note.



I make simple result in excel File

please pay attention to  this result
it is output formula 
 out = (4 * avgADC0 + 6 * avgADC1 + 6 * avgADC2 + 4 * avgADC3)/6

it is 75% overlap 



it is 20% overlap