Not as far as I am aware, the media type dictates how much ink is laid down, it has nothing to do with a 'default profile', when the chart is printed it needs to be printed with no colour management either by the application or the driver. I still do not understand where you are getting this 'default profile' from.For example using the Colormunki, when you initially print the test chart it brings up the default printer dialogue where you pick the closest paper type. This is the default processing/hardware settings the custom profile is based on
Eh? Bullet point 3 is simply saying to note the settings used in the print dialogue so that the same settings are used when printing using that profile, nothing to do with soft proofing....Bullet point #3 is basically saying that if you softproof using your custom profile and print using the same printer dialogue settings the results should be the same... they are the foundation of/part of the custom profile.
To repeat:
In LR when you soft proof a virtual copy is created which gives you a simulation of how your file will print using that profile, you refine the soft proof to give the best result that you can, this may involve adjusting contrast, pulling some out of gamut colours into gamut etc. these refinements are carried out on the underlying file.
For that file to print correctly it needs to be fed to the printer driver via that same profile which you select in the print module.
I really am having difficulty understanding your interpretation on colour management and the use of profiles.
BTW did you know that the new software for the i1 Studio works with the ColourMunki Photo hardware...