Definitely go north to south, that is the most predictable wind pattern of all the USA touring routes, wind from the Northwest (tail).

A May start should be fine. You might have rain in WA/OR, but that's true in June too.
Here's a link to a weather resource, this shows monthly average temp & rainfall for Astoria Oregon.
http://www.weather.com/weather/wxcli...graph/USOR0017