What you really need is a whole different world war, and a whole different system of alliances. Indeed, you need to make America much more prosperous early on in some way, so that by the end of the 19th century the spread of its economical influence would seriously threaten both British and German commercial interests.
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In this case, it would indeed make sense for the Europeans to draw in (a much more stable and coherent Porfirio Diaz-era) Mexico.
A much more prosperous America probably involves it eating Canada and Mexico at the requisite junctures you know

(most probably Battle of Quebec in 1775, and sometime around the actual Mexican-American War because I really don't buy into the theory of Canadian land diverting American settlers from Texas all too severely, because immigrants could've gone there to begin with and didn't much).
War of 1812 probably never happens as a result of no Canada to want to annex, presumably America either stays neutral and gets the Louisiana Purchase or for some reason sides with Britain and just up and takes it (because it's useful and France is distracted). All that Manifest Destiny jazz. Settlers wind up going to Texas anyway because frankly only so much land in Canada is arrable, America says "Hey, great, Mexico, lets take their stuff too," as in OTL. Civil War either happens and the South is more quickly crushed as a result of even grander Northern industrial capacity or is smoothed over somehow. Maybe that talk of buying Cuba goes through. Regardless, slavery kicks it at some point. Sometime in the later 1800s Mexico winds up being gradually absorbed in a series of expansionist adventures and partitions, maybe along with bits of Central America, and other American imperialist adventures of the period go through too. At some point Alaska gets purchased. End result being the US owning most if not virtually all of the North American continent.
Now, if that happened, I could see a coalition against America by the sea powers. It would be a rather interesting war, if only because America would be stupidly powerful, and could probably win the support of the enemies of those sea powers: France and Russia. So, you'd have a lineup of America, France, Russia vs. Britain, Germany, Italy, Spain, and Austria-Hungary. Japan would probably side with the latter if anybody, though maybe the former depending on the precise circumstances of colonization at the time. A much more proper World War I than its real-life analog, frankly.
America would of course be lead by Teddy Roosevelt whenever a showdown happened, because could you tolerate anything else? The actual war shakes things up dramatically somehow or another, with a game set after that probably (not before, or you'd get some silliness like DaNES degraded into). In my opinion that kind of lineup yields a mostly inconclusive bloodbath with a big land war in Europe and a lot of naval action and some sneakier incursion and raid stuff around North America.
I rather like this idea after having outlined it thusly and think somebody should develop something along these lines. That's a late Industrial setting I'd actually be willing to play.