Geography of the Prescott's trek

Love the movie but I've never understood the geography of the move to the Prescott's farm. Did it make sense and I'm just missing something, or was it just some minor sloppy writing? Since they took the Erie Canal west to start, and finally ended up in Ohio, it seems like they would have had to take their little raft along the coast of Lake Erie to get to Ohio. Wouldn't all the rivers at that point be flowing into the lake, thereby requiring them to go upstream instead of down (which they repeatedly say is their direction of travel) to get to the interior? On my last viewing, it occurred to me that we might not have been shown not only the trip on the lake, but a trip upstream into the interior and an overland trek before they get to a river which they then take downstream toward the Ohio. The problem is, that would make nonsense of the idea that Linus is going in the opposite direction on his way to Pittsburgh. I've also never understood how both Linus and the Prescotts run into the same pirates while heading in opposite directions.

Seems almost as if it was originally written with both parties heading upriver and then got changed, whether to add the scene at the rapids (which only makes sense on a downstream trip) or because it was felt that the Linus-Eve story worked better if they were headed in different directions and not just traveling separately.