Remove DC offset from op-amp output to allow increase in gain
There should be no change to the DC output voltage of X2 when you reduce R3. Either the 680p cap is shorted or there is some other difference not shown on the schematic. The offset should be dominated by the bias current x 1M, approximately.

Edit:

Given the very low typical bias current of the TSV992IST op-amp you are using, the offset will be dominated by Vos of the op-amp. Output offset (relative to junction of R5/R6) should be significantly less than 10mV at or relatively near room temperature with that circuit.