I don't understand why you think the documentation is "slim". There is a 92 page manual for the MCT, within which there are some references to the basic printer manual for topics the MCT manual leaves to the main manual. So altogether, a considerable amount of detailed guidance is available.
The MCT brings together in one handy Custom Media file all the information ylu build in to that file regarding paper feed adjustment, advanced printer settings, advanced paper settings, calibration target and ICC profile. You also need to update the new media information file into the printer driver following their instructions in the printer's own on-line manual. Once you've done all that, if you call-up the custom media for printing, all the associated settings including the chosen ICC profile should be loaded and ready to print with.
To use custom profiles for a custom paper type, it appears to be inferred from the warning messages in the MCT manual that one needs to make sure the settings in the Advanced Paper Settings sheet are the same as the ones that were used for printing the profiling targets used to make the ICC profile, otherwise the profile may not accurately characterize the ink laydown of the printer. As I have not experimented with this procedure to see what happens in the event they are not coherent, if any one else has it would be useful for them to join this conversation and contribute and evidence-based a view on this matter.