An abort button makes 9 buttons.  The abort button stops all the desks.  There's no abort button on the OEM keypads but it might just use any button press as an abort.

Selecting the desk is trending towards a home made multimeter type dial.  It would use a hall effect sensor which detects 4 angles.  A spring loaded ball bearing would click into 4 positions.  It would eliminate the glitches of wipers & pots.  Multimeters & cameras have used dials forever.  They're just large.  A Fluke clone with a dial on the bottom & 2 rows of 4 buttons on top would provide the basic functions.  The abort button could be on a corner of the dial.  

4 presets might be enough, in which case abort would be in the 2 rows of 4.  Things get more interesting with 4 presets, full up, full down, sitting, & standing.  3 of the desks only need 3 presets.  The dial could have 5 positions with 1 position being 4 more presets for 1 desk.  Having abort in its own area would make it more obvious though. It could just be high vis filament.

There isn't any more store with vintage knobs nearby.

The fluke sandwiches an inner liner between 2 halves of the dial.  

The outer case creates the detents with a symmetric teflon spring.  Lions don't have teflon.  They only have PLA.

To make memorization of 4 presets for 4 desks easier, they'll be limited to 4 presets. The presets will be the same on all 4 desks with minor tweeks.  Some presets will be duplicates.