What is the best way to remove the non-rejected portion of a common-mode voltage and any bias voltages from a differential voltage measurement?
SSRs can have a diode drop accross them and may not work at all below some current level.

Step back and explain what you are really trying to do.  I'm guessing you have a stack of 12V batteries and want to find the voltage of each one.  What about a small micro on each battery that reports the voltage occasionally via UART thru a opto coupler?