Well, just to do some more math for the fun of it...from where we are now, we're supposed to walk 3 to 5 X along the river, and then 1 or 2 X away from it. Let's assume that we're talking about a right triangle for simplicity.
If we could somehow get a precise bearing on the lodge and go there, we're talking about:
[spoiler]
Following the River | 3X+X = 4X | 3X+2X = 5X | 5X+X = 6X | 5X+2X = 7X |
As the Crow Flies | sqrt(10)X = 3.16X | sqrt(13)X = 3.61X | sqrt(26)X = 5.10X | sqrt(29)X = 5.39X |
Savings | 0.84X (21%) | 1.39X (28%) | 0.90X (15%) | 1.61X (23%) |
[/spoiler]
(You can look back at my earlier math for the times associated with each of these scenarios.) The point, however, is that going cross-country doesn't gain us much--about a quarter of our remaining planned hike in the best scenarios, less in the more probable ones--and seems very likely to result in the GM calling for rolls to determine how lost we get.
I vote we stick to the river. Very hard to get lost that way.