Dathi THorfinnsson said:
Remember that American Rugby IS gridiron - or at least that's what it's evolved into.
So. Basically, you need to stop the evolution away from the ancestral English format. (Which seems to be still have been in the process of codification.)
Note that the earliest 'football' games in the US were what we'd call soccer - no carrying the ball.
Then McGill introduced Rugby to Harvard, and it is that game that grew into gridiron.
According to what I can find, Walter Camp is the person responsible for the major changes that led US Rugby/Football/Grid iron to evolve into a completely different game.
Have him not get involved, and you might have a chance for international rules of some sort to lead to a common game.
Works for me.

Would you rule out two or three "rule sets" competing, with Camp's OTL set losing out? (I'm thinking of a parallel with OTL baseball. I presume there were enough rugby variants around.)
I stumbled on
this thread, proposing the development of American rugby, with a 15-man side, based on Welsh immigration (
per Argentina); AIUI, the Argentine game developed thanks to UK railway workers building the local network, so immigration alone wouldn't get it. What would you say?
Any thoughts on rules? Style of play? Particular "movers" in TTL's game, akin to Camp, who'd move the game away from OTL rugby without getting to gridiron?
On the technical side, given deaths in the game were pretty common into the '20s, what would you say about the gear in the new game? Can rule changes prevent deaths, or do you need to add pads & helmets? (Frex, a "no tackle" rule? Or a change from scrum to "bounce" to start play?) If gear is "mandatory", does it (necessarily) develop more rapidly if gridiron doesn't happen? (My sense is, rugby is rougher, so it pushes things harder.)