hi,
What voltage do you measure on the actual HE output, ie on the non invert pin of the OPA.?
Try to connect a 10K from the output of the OPA to 0V.
Have downloaded the pdf, will look thru it.
EDIT:
Looking at the HE d/s, I see that the output swing is about the Vs/2 level, so for no field the output is +2.5V.
The Gain at the non invert is 1+ [Rf/Ri] ie: 2 with 10K's
So the Vout would want to drive to 5V, to offset this would require +5V from the Vref OPA, which it cannot do as at 5Vs , the max is +3.5V.!
One way would be use a resistive divider on the HE input, say div by 2, so that Vout would be +2.5V with no field.
Apply an offset voltage Vref of +2.5V to bring the Vout to ~0V.
The LM358, IMO , at 5Vs is not suitable for the project, either a rail2rail or a higher Vs or a -Vs dual supply.