Having a 2nd admin page for a custom post type

Yes, that is absolutely possible.

Have a look at the add_menu_page() function and use it like so:

add_menu_page(
    'My 2nd CPT Menu',               // page title
    'My 2nd CPT Menu',               // menu title
    'edit_post'                      // required cap, same as in register_post_type()
    'edit.php?post_type=yourCPT',    // edit.php + query string as slug <-- this is essential
    '',                              // empty callback
    'relpath/to/icon.png',           // optional icon file
    101                              // optional menu position
);

Analogously, this can be done in a very similar fashion with submenu pages.

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