The motherboard replacement did not appear to solve the issue.
In short, after some testing the port(s) affected seem to reliably work with Ubuntu and certain specific version of Intel’s GPU drivers, but present issues with most other versions I’ve tested (e.g. with the version installed by the driver bundle they very reliably do not produce an output at all, despite detecting the monitor).
I have recapped my experience thus far in this thread.
I’m still in contact with support for possible further troubleshooting.