I know that a uniform profile would work, but I'm trying to use keycaps that I currently own.
Here are some diagrams of the MX stems/keycap dimensions to prove my point for those non-believers.
Show Image
(https://telcontar.net/KBK/Cherry/images/MX/Cherry_8_mm_mount.svgz)
Show Image
(https://i.imgur.com/iX8JW.png)
And what is that image supposed to prove really?
The MX standard specifies that the keycap stem is symmetrical. You image shows it as symmetrical.
That literally means you can turn a spec compliant keycap any of the four ways, regardless of the width and spacing on the switch stem, which you correctly state is non symmetrical. Its is, but it doesn't matter if the keycap is following spec. A non-standard keycap not following spec though, then it matters.