Actually the information about putting the calendar short code in a page template is intended for displaying the calendar on the front end of the page.
The events information already displays on the user profile page. Are you not seeing it there?
A short code really shouldn’t be used in this case. Since your client prefers the way the short code displays, you can create an admin page that loads in the same templates, scripts, and functions that the short code does. Kind of the same principle outlined here:
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