Paulj
To determine the beginning of the Missouri you would have to map every fork, every branch to the end. How do you determine the farthest (or the longest) root of a tree? Then the weather effects water flow. Here east and north of Idaho Falls up in the Yellowstone plateau and western WY the average snow pack was 165% of normal last winter plus we had a late but rapid spring thaw. How does that effect the water flow from an area maybe 200 miles away that had only 80% of normal snow pack? That will also change every year.
L&C knowing that every mile they went south was a mile farther to travel to get to the mouth of the Columbia River plus thy had to get to there before winter, I feel that probably Lemhi Pass and the spring was a compromise by L&C.