Did you try pulling down LPMB and pulling up SLRFTB? That might help mitigate the problem a bit. Another alternative might be to try and isolate the wire away by using a teflon-coated needle, but ultimately with a coil of solder wire you're adding a big antenna to the circuit, so I'm not sure that you can really get away with it.
Edit: Another alternative is to not rely on contact with the soldering iron as a trigger for the feeder mechanism. The only automatic dispensers I have ever seen use a foot pedal, probably because the flow of solder would be too unpredictable otherwise. Perhaps consider using a different approach where you control the motor with your body instead (e.g.: still using a capacitive sensor, but requiring your hand or fingers to touch some surface in order to trigger the motor).