Schmitt trigger

You are correct in that the carbon pots are a cheap part and probably not best suited for controlling large industrial motors. When I began retrofitting this control panel, every one of them was so noisy they were unusable; a bit of sideways pressure on the stem would cause up to 30% noise. I washed them out with alcohol and now they are actually quite good in therms of noise. I am guessing that 10 years down the road they will be bad again, which, as you pointed out, simply isn't the case for wire-wound pots.

One issue that wire-wound pots won't solve, though, is the fact that similarly to carbon pots, they can be positioned near a switching threshold. Say for example you scale a 3.3v output by a factor of 10 and quantize that by converting to integer, getting 34 discreet steps. If the scaled input voltage from the pot is at 9.99 it will inevitably cause erratic switching between 9 and 10 because there is always some noise in the circuit and the logic has zero hysteresis.

An ideal solution to this would actually be a rotary selector switch with as many switch positions as you want the control to have in the first place.

Consider replacing the pots with binary coded switches.
www.jaycar.com.au/4-pole-sealed-pcb-rotary/p/SR1216

You can decode the outputs with one of the mux components and 4 input pins will give you up to 12 different discrete values on each switch.

I am considering doing just that... I would need one with a 5 bit output and more positions, though.

The one I posted had 12 positions.
Surely a 16 position switch would be enough? That only needs 4 outputs.
www.mouser.com/ProductDetail/NKK-Switche...YrFeQ53PNxELVP6Jw%3d

Yes, those might work. My “need” is based on what I asked the machine operator what they would like and is also subject to part availability and number of available input pins.

An ideal solution to this would actually be a rotary selector switch with as many switch positions as you want the control to have in the first place.

Well, yes, but that's cheating because you asked how to do it with the analog wiring you already have in place.

If you're going for digital instead, then you have the option for a rotary phase encoder instead of selector. Then you only need two digital inputs for any number of selections instead of log2(selections). You keep and display the state of selection in software, so you can change it anytime without fussing with the physical wiring. You keep the satisfying physical knob, but you do lose the satisfying physical display of the setting.