Eric, I think that's still a feasible plan. You won't have to worry about snow from Vancouver to the Columbia Gorge, however, once you hit the higher elevations in the intermountain West, you still run into the risk of snow, even in late April through May. (Heck, depending where you are, even June.)
But is starting in the East a deal breaker? Getting to the NW in August, the weather will be great-sunny and highs around 70-80. (Of course there's always a shot of rain, but it's pretty small during the height of summer.) You'd also be able to cross the gorgeous mountain passes of the Cascades without worry of snow.