Automatically extract cookie from Firefox
As far as I know, Firefox stores it's cookies in a SQLite database. You could display a ff-profile-selector under the manual instructions and then extract the cookie from the selected profile.
That could be a really good idea haven't yet looked on how to do that but that's definitely an option.
If I don't forget it, I'll look up the query today.
Which cookies of the 62 are needed? In firefox's database (~/.mozilla/firefox/<PROFILE>/cookies.sqlite) they are are all saved as host = '.youtube.com' in the table moz_cookies:
SELECT * FROM moz_cookies WHERE host = '.youtube.com';
I found that this query removes most unnecessary cookies:
SELECT name, value FROM moz_cookies WHERE host '.youtube.com' AND originAttributes = '' AND value != '' AND isSecure = 1;