Thanks Predrag, that gave me an idea. I found some instructions over on the LiveComposer Help site on how to add LiveComposer support to custom post types. I've configured this for CoursePress Pro courses and it appears to be functioning correctly now.
It would seem that with LiveComposer, the LiveComposer Blank theme and CoursePress Pro combined it's possible to design an education platform from scratch without the need to manually code and maintain a custom theme.
Thanks for your help. I've done as you suggested and allowed access to the website. If you could investigate and let me know would be most helpful.
I've found a more appropriate builder plugin, but am still having the same issue of CoursePress Pro plugins not appearing as valid post types.