Auto Offset

I'm using a LEM current transducer to measure pulsed currents.  The 
current sensor produces a current output which I feed to a resistor 
producing a voltage that represents the current flow. The voltage feeds 
an opamp for offset correction and buffering.  The sensor has good 
accuracy (+/- 0.5%), but suffers from an initial offset  
(+/- 0.15mA) and worse, a thermal induced offset (+/- 0.35 mA over temp).

Since I know when the current pulses are coming, I want to to force the 
offset to zero before taking a measurement.  I've seen circuits to do 
this using the following techniques:

1. An A/D followed by a D/A.  With zero current input, the offset is 
driven to zero, and the offset correction is latched in the D/A until 
the next "calibration" cycle.

2.  A/D and a digital pot controlled by a processor, works similiar as 
above.

What are the merits of either method.  I prefer not to have a processor 
involved, but do have access to FPGA resources.

Is ther a simple way to do this?

Mark