If American settlers are not stopped at the Appalachian Divide they will need passage down the Mississippi River to make the Ohio River and Tennessee River Watersheds profitable. To ensure the security of the Mississippi River Americans will need at least New Orleans. New Orleans also brings in the Florida Parishes of Louisiana which at the time were the far west of West Florida. This will put heavy pressure on the federal government to annex East Florida, if a portion of West Florida and all of East Florida are annexed then the rest of West Florida will be sought too. Also, if Americans can get beyond the Appalachian Divide they will want to possess the Great Lakes and St. Lawrence River watersheds - which also brings the Maritimes into play. If they obtain those then the Hudson Bay Watershed is effectively theirs.
If Americans settle on the east bank of the Mississippi River, they will have squatters illegally immigrating into territory on the west bank of the Mississippi River. A competitor state with access to the Great Lakes (for example Canada) would have more difficult logistics of moving settlers from the Great Lakes down towards Arkansas than if they were coming west from the United States. If America has possession of New Orleans, it will also have the ability to control the economic development of the western half of the Mississippi River Watershed. This also makes the western portions of the Hudson Bay Watershed vulnerable to American settlement.
If Americans can take the Red River it is very easy for the Rio Grande Watershed to fall under American influence too. Americans were sending people into Oregon Country by the 1810s, and I think if it weren't for the War of 1812 they could have had a much more rapid settlement of the area. So a Texas power, and a War of 1812 analog could turn the Rockies into a border for the Americans. A Cascadia Power would certainly do the that trick. American migrants could find their way into California, not assimilate, and eventually take it over, but I doubt that effort would go unnoticed by whichever country controlled California. Trying to fight a state level war out in the Great Basin would suck.
If Americans get into Cascadia then the Gulf of Alaska and the Beaufort Sea become targets for Manifest Destiny. If Americans obtain control of the Rio Grande River that puts the Colorado River, the Gulf of Cortez, the Great Basin, and California in play. Americans could also create a larger empire headed south.
So you aren't going to get a military force strong enough to check the Americans at the Appalachian Divide without altering some of the fundamentals about the American Revolution. This means to me, that the Americans will eventually fight a war to control the western half of the Mississippi River Watershed if they can't obtain it peacefully. Maybe the Iroquois and the Cherokee could find a way to come out of the American Revolution exponentially stronger than they were going into it. Maybe there is a Huguenot State in Texas. Maybe a United Iberia has made a very strong mercantile Viceroyalty of Tejas. Maybe Spain, Britain, China, or Japan could put a thriving colony in Cascadia by the 1650s.