Use a MUX. You only need one MUX channel per battery joint. One channel can support the + end of one cell and the - end of the cell above it in the chain. The easiest MUX type to use for this is a FET that you control ON and OFF at each battery joint. Alternatively use an analogue switch at each joint. At any given time you would have two of the FETs/SWTs on at a time. Feed the downwind side of the MUX over to an A/D converter that is setup to make a differential reading. This will remove the common mode voltage by analog subtraction and leave you with full A/D resolution for each cell.

Michael Karas