Wind formulas assume equal amount of wind from shooter position to target. Breaking down sections from the rifle to the target can be tricky. The wind ALWAYS has more effect on the bullet closer to the muzzle when shooting across winds coming from the same direction.
I do most of my shooting in heavily treed mountains with large expanses of nothingness in the middle. The wind never blows the same speed for more than a minute or less. For your shot, I would have done much like you did, but from the position that the canyon is a full value 12-15 wind with the side I'm shooting from blocking a portion of it. I would pick the high or low number, and fire when the wind at my position matches the condition I picked. There is a large amount of SWAG in long range wind calls in the mountains. The river analogy is a good one. If the canyon is straight, with the prevailing wind blowing perfectly up or down it, wind shooting is relatively easy. If it curves, or has perpendicular ridges jutting out, or the wind is cutting across it at an angle, your call will have to be thought out more carefully.
Heavy opposing winds are very rare in the mountains. You are more likely to run into a wind running full value from one direction, and an opposing thermal coming from a slight or heavy angle, but in the opposite direction. If you are on a heavily treed hillside, it might feel like a wind coming from the right, but it is a swirl created by a basin above you bleeding down from a left wind in the canyon. I always look carefully at the target area to see if the wind direction is the same as where I'm shooting from. When I was with Ryan on the moose hunt one time, I watched the wind change directions on the side we wanted to shoot, while the wind stayed light and from the same direction where we were set up. Think back to the river analogy, comparing the wind to eddies and swirls running in the opposite direction of the current. In that case, I ignore the breeze where I'm at and shoot for the best estimate on the opposite hillside.
There are a couple of places I hunt that require me to ignore the wind at my position and shoot in the opposite direction (but only in May, and only when there is a low pressure system sitting on me!)
Every terrain feature and location is different. That's why they hang wind flags at ranges in intervals and the most competitive shooters keep notes on those particular wind flags and the shots they took. You can do the same without wind flags by practicing in the canyons you hunt. Remember to keep in mind your rifle's max potential accuracy at distance. If your hits are within that bubble ( 1/2, 3/4, 1 MOA, etc.), you are doing fine. Keep good notes!