measuring the input Z

You could place a pot in series and adjust Vin to 1/2 Vg then the pot would be equal to Zin. If you use this approach and do not measure both points as you adjust the pot you will have an error 600 Ohms. Remember maximum power transfer is at the half power point. If Zin = Zout the drop across Zin is 1/2 the supply. In this case Zin=Rg + Rs. So the point where we match the impedance is not determined by the pot alone.

I have the generator set to 10mv and have a measured Vg = 9mv I'm losing 1mv across the gen resistance.

Here I reduced the resistor and read Vg and Vin.

I increased the resistor and measured Vg and Rin.
The point where Rs = Zin would give the best results. Setting Rs to drop 1/2 Vg gets us close to that point but Vg varies with load so it is a juggling act. Using two meters and adjusting for the same reading could be an acceptable alternate.