Analog sampling over long lines freezes ARM chip

OK, here's the actual schematic. 6 long wires are attached as two 3-conductor signal cables, and their ends are contacts that a rolling metal object may connect. Wires are what they are, my device connects to them, replacing an old analog circuit. The wires are connected to "top line" and "bottom line" connectors. For those not familiar with the SAMD21G18 chip, the pins that T1, T2, B1, and B2 are connected to are analog inputs.

There are several "event" scenarios, and most include 3 wires. Events I am sensing have limit of 100-500 ohm external resistance. Putting 1 k resistor in line would seriously reduce the sensitivity...

This has been one of the most "fun" projects since I can never get the device to freeze on the bench where I have instruments and computers to attach to serial or USB ports for diagnostics, but it easily happens in the actual environment where bringing computers and instruments is a big bother.