Level shifting with a voltage reference of 1.6V
Where you indicate you are connecting to the diode string is not the right place. It should be between the anode of the top diode and the current limiting resistor.

What is the signal source? Specifically, what is its output impedance? This appears as an additional resistor in series with the 75 K going off to the left (please add reference designators to your drawing), and affect both the overall circuit gain and the value of the DC voltage added.

The non-inverting input of your opamp circuit is not a virtual ground, so there is interaction between the input and offset signals.  The two 75 K resistors form a voltage divider for both.  This will attenuate both the input signal and the DC offset voltage (assuming the input signal reference potential is GND).