I think the gravel road running through the property works as a sort of swale and the sage brush growing down slope is indicative of the type of plants that could survive your minimal annual rainfall. 12.5" average is not much. I live in northern colorado and the sage brush landscapes are very similar throughout Colorado and Wyoming, with shrubs/trees growing only in the hillside valleys like your property. Maybe you could use that to your advantage?
Also, aside from the water draining into those valleys, snow also collects in drifts in the valleys and melts slower/stays longer. Tree shade can hold the snow longer. You might see if there are some evergreens that survive in your dry climate to hold more snow in the valley later into the spring. There is probably a Montana University Extension that could help you out.
Also, not sure about Montana water rules, but in Colorado, installing or modifying surface drainage and stream beds to retain water might be illegal since it messes with downstream water supplies and water rights. One thing to check is if the source of the water on your property is part of a mapped stream. If it is, it may be part of the US Army Corp. of Engineers "waterways of the United States" which would be a major headache. This stuff gets complicated quickly.
Also, it is hard to orient the picture to the map. I assume the map has north ttoward the top of the screen. Which direction are you looking at in the picture?
