There will be a certain magnetical coupling of adjacent twisted pairs in the low frequency range. The effects you described in your previous thread (varying signal when moving the cable of your LVDT-like sensor setup may be caused by similar effects. But it may be also caused by more trivial varying cable capacitance, changing the sensor load.
Before applying arbitrary changes, e.g. using common mode chokes or different cable, I would try to verify possible crosstalk pathes by specific measurements. If it's actually crosstalk, using separate Rx and Tx cables may be a simple solution, however.
Likely. What's against using a truely differential driver and differential sense amplifiers?