Macintosh HD is not visible on boot but is can be detected using Recovery on an installation USB

Solution 1:

So as it turns out, there was nothing wrong with the SSD or any boot parameters.

The SSD that used to be in the MacBook was running Yosemite, however the one that I was putting into it was running High Sierra.

I solved the issue by putting the original SSD back in, upgrading that to High Sierra then putting the other SSD back in, which was detected immediately and booted instantly.

My best guess is that there may be some form of OS protection built into the system that detects when an older/newer OS is present and acts accordingly. It would be nice to know exactly what's going on there, but for now this has solved my problem.