The best way might be for it to not develop in America at all. Just take the story of American football and move it to say, England. Rugby just needs to develop along a similar path as OTL. Rugby league, with rule of six. Some prominent team builds an expensive (and the first) permanent concrete rugby stadium, while at the same time, some fatalities cause the Prime Minister to consider banning the sport. Rugby league organizers want to widen the field to open the game up. Because of the concrete stadium, this is deemed impossible, and TTL's version of Pop Warner suggests that forward passing be allowed. To make the game harder, the rule of six becomes the rule of four, and the number of players is dropped from 13 to 11. Now this rugby develops like OTL American football. Passing and running become emphasized over kicking, the rule of four becomes four downs, etc. etc. while the game spreads to first English possessions- Canada, Austrailia, New Zealand, and then around the world.
ASBs? Maybe. But then again, it's the reason American football is the way it is. American football got to dangerous, Walter Camp wanted to widen the field, but a brand new concrete Harvard Stadium meant there was opposition to that, so someone (I think Warner) suggested the forward pass instead. Voila, American football.
The other option is more limited, but it involves the US using football, rather than baseball, for diplomacy. So teaching football in the Caribbean, star football players traveling to Japan after WWII, etc. etc.