I would be inclined to put the resistor on the arduino end rather than the remote end.
1M is still quite high and you will get a decent amount of pickup with that.
The fact is that your circuit is not suitable for what you are trying to do with it. You need a buffer amplifier on the output of each sensor before feeding it along a long wire.
As previously noted it is in impulse detector not a push sensor.
After lots of experimentation with an electronics lecturer
Familiar with an arduino or not, he is not much of a lecturer as this sort of thing happens with all circuits.