I know there were some early treaties which noted that the Ohio and Mississippi rivers could only act as a boundary, nevertheless. What kind of yield in U.S. history would it take to have a state or states where either the Mississippi or Ohio is included within a state's boundary?
Depends. It may not be too hard with, say, Kentucky or Missouri, for example: particularly with the latter, if you can somehow create a movement that convinces southern Illinoisans that they would somehow be better off as Missourians. And one thing that can be done with Kentucky is annexing southern Indiana. Two ways this can happen are, if the Bluegrass State stays with the Confederates during an ATL Civil War, and their side wins by more than just a small margine, or if someone comes up with the idea to enlarge the state of Kentucky by going northward(up to a point!) before the Northwest Territory can be carved up into anything outside perhaps Ohio.
Other than that, though, you'd need to make a LOT of changes to make any other non-OTL scenario plausible.