Weak Sensor Signals across Long Distance Wire

When people said put a 1M resistor across the the piezos they meant across each individual one on the input side of the multiplexer.
You have lots of unterminated inputs to that chip and the cross talk will be bad.

I've seen a lot of people here use the word random or 'noise' when referring to the floating input.

It is random in that it is not predictable but it is not statistically a rectangular distribution.

I've just seen those Fritz diagram around here before, so I thought they were the standard,

Yes you do see them. If I had my way they would be banned. Most others think that as well. They are a sort of write only diagram. In other words while you can create them they are almost impossible to read except in the more trivial cases.