Thats more of an indictment on the way the Super League has been run, that they let their brand be taken over by Football. Possibly time to rebrand as NRL Europe, so they can actually market themselves in the UK effectively.
I wouldn't be too worried about people searching Super League anyway. If a CFL game was played as a warm up to the NFL in Australia, you wouldn't get a whole heap of people searching for CFL. Most people are going to watch the main event. + I think they may realise they weren't watching womens football and add 'Super League Rugby' to their search in that case.
MLR, RFL, NRFL are all very clearly different branding to the NRL, 4 letters or vastly different in spelling. Thats why you hammer the NRL branding. It's NFL, but with one letter difference - easy to remember. After you've built exposure to the existing Rugby market in America - you barely mention that it's Rugby. It's just NRL.
You think the NFL cares that there are 50000 leagues with 'FL' at the end of their name in Australia? Different scales, but you get the point. Get the casual viewer that cares to know, that the NRL is the Premier Rugby competition in the world. That's how sports work in America - 3 letters and they want to see the best in the world - not too different from Australia honestly.