Jason,
Here is some hints you can test to get rid of the switching pop.
Probably there are some dc shift on the Melcor op-amp + input, when you switch between the transformer secondary low resistans and the 1 mohm ground reference in DI mode.
So try to move the 0,1uF capacitor from the DI input (before the switch) and instead connect the 0,1 uF capacitor direct after the switch. (before the 1 mohm resistor)
If you still have a small amount of switching pop, you can connect a resistor approx. 4,7 to 10 mohm, before the 0,1 capacitor to ground. (next to the switch)
But first of all, you shall check if you can adjust the offset setting, the R4 resistor connected to the "trim" pin on the op-amp, so there are so near zero dc voltage possibly on the output.
If there are high offset voltage on the output, you can also get pop/scrape in the gain setting switch/potentiometer.
Can you show the gain setting circuit for the AML-27 ??
--Bo