Op-Amp Design Resistor Values vs. Actual Values - Gain Calculation
First, look at the signal gain from the non-inverting terminal (setting the rheostats to 0)

$$\dfrac{V_{OUT}}{V_+} = 1 + \dfrac{69k}{10k+1.91k||10k} = 6.95$$

The voltage at the non-inverting terminal is

$$V_+ = V_2 \dfrac{69k}{10k + 69k} =  V_2 \cdot 0.873$$

The overall signal gain is thus

$$\dfrac{V_{OUT}}{V_2} = 6.95 \cdot 0.873 = 6.07$$

Which is very close to the desired value.  How did you arrive at the conclusion that 61k and 10k should give the correct gain?