There's the Linux route, since it's an Intel (or ARM) laptop. I work for a corporation, so I already live under a "regime" of sorts.

Problem found & resolved - I was using two USB-C to HDMI "dongles", and even when using two of the same brand, the freezes persisted. If I use a single USB-C dock (such as the Dell D6000, multiple monitors are supported and the freezing behavior has stopped)

@Savami, try using a single dock that can support both monitors. That solved the freezing problem for me, when I switch to a Dell D6000 dock in place of the separate USB-C dongles