I’m getting a noisey/square wave output for the mux/demux

There's a few questions in there, so I'll address them one by one.

What does A x B : C Mean?

Read this as A instances of a B number of inputs to C number of outputs. What you are looking for, if I understand correctly, is a 16x2:1 or a 32x2:1 chip. If C is more than 1, then your chip is significantly more complicated - you would no longer be selecting one input and connecting it to the output. Which leads well into the next sub-question -

Why are there $200+ chips for this simple function?

The specific part you linked is a 1x32:16 wide-bandwidth, DC coupled, buffered, video MUX, which can select any of it's 32 video inputs and output them simultaneously on it's 16 buffered outputs, with a gain of 1-2x. You could sorta think of it as a 16x32:1 with a lot of features. It's got quite a bit more inside than just CMOS switches. It isn't really designed for your function, which is...

How do I connect two memories to a master CPU

The most common method for hooking up multiple memory chips to a driver/controller/cpu is to use a tri-state bus. The address lines drive both chips, and the data bus is shared between all chips. Both chips should have a pin like "output enable", which can be controlled by the CPU. I found this article discussing memory buses at a rudimentary level - it has descriptive images. See Figure 8 for the gist of what I think you want. It is the simplest way of hooking things up, and the way I would recommend if the chips support it.

How would I make one?

Well, I think you were on the right track. CPU buses can be bi-directional, so intercepting the right output enable signal may be risky. The part you were probably looking for was a digital switch, something like this 16x2:1 FET mux. This is the cheapest one at $1.75 each. Wide bidirectional buses are best handled by ICs.

Note

I would check with the maker of your CPU to look for app notes and reference designs regarding memory buses. That will be the easiest way to see if you're on track.

Trying to send these kinds of signals 30 feet all together on the same cable is nuts. A much better overall architecture is to send power and simple digital serial signals over the cable. Handle the details of the stepper control and sensor readings at the far end of the cable, and receive commands and send results digitally. With the CAT5 cable you described, you can use one pair for transmit, one pair for receive, and the remaining two pairs for power.

Russell has described some things you can do to try and make this mess limp along. Maybe if you're careful those are good enough. However, the real problem is in the higher level architecture, which is where any real fix will have to be made.