I added a custom-convert.conf to piCorePlayer, restarted LMS, and the custom settings worked as expected.
(I added the file by manually placing it into /usr/local/slimserver, because trying to upload it using pCP's Upload option kept giving me an "Invalid Format" error).

But when I rebooted the machine, the custom settings disappeared.

My settings are stored on an attached USB disk:
Name:  pcp.jpg
Views: 185
Size:  25.6 KB

I presume that I need to force the custom-convert to be copied to the USB disk to survive a reboot, but how is that done?
Do I just click the "Move LMS Data" button, or is there something else that needs to be done?
Do I also need to backup to the SD card?