Unfortunately the RS have claimed the city's name for their team.
I'm a wool (apparently).
And from my position, the term Merseyside refers to a vague, fuzzy area centered around the Liverpool/Wirral. It's imprecise, and if that's what you want then...fine.
Scouse, to me, is equally imprecise.
I think you're deliberately overstating the knowledge and intelligence of Americans. Yes, many of the 'Ivy Leaguers' are super intelligent (or wealthy). The rest voted Trump.
Only people from 'Scouseland' would believe that The Mersey is the centre of the Universe and yes.
I, personally, wouldn't mind 'Mersey' within a broader package of regional one-upmanship slogans (below the top line but subordinate to it.
We are...
Everton: Liverpool's Premier Club.
Everton: Liverpool's Original Club.
And yes, if you wish, in merchandising...
Everton: Merseysides Premier Club