Added diff amps are un-needed and unwanted. Use analog mux directly from the sense terminal pairs from each resistor. Also, unless you have gain in the first stage of your diff amp all you will do is add noise. The source impedance is low enough that buffers are not needed nor wanted.
In the common circuit for a frequency standard, you need to modulate the VCXO. The loop locks to a tiny fraction of the line width. Any even order nonlinearity in the VCXO shows up as a frequency offset. In the short term, the noise on the output of the standard is the noise of the VCXO. You need to have a very linear and low noise VCXO. The servo loop of the standard only starts to take out the noise at frequency offsets under 1KHz.
Given choice, i would use ratiometric methods. I can get the same or better speed and the same or better resolution with better accuracy. Plus i get it all in one conversion instead of 4.
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