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Look for these.
I have abook called the okanogen mule deer,it has their migration routes,it was put out by game dept 1978,106 pages
I would bet there probably have been some studies on radio collared deer used to track their migration routes. I know where I hunt in Idaho the whitetails migrate out of the High Country to winter near Grangeville & their migration has been studied by using collared deer. Good Luck & let me know if you find anything for E. WA deer. You may also want to check with area biologists.