most oregon state park campgrounds will have spots avaiable on a first come first serve during the week. we do this all the time. especially tues, wed and thursday. So given your plans to find spots during the week, you should be able to find something.
However, weekends are another issue, usually reserved full well in advance. your only hope is finding a camground where there is either a cancellation or a no show from the previous night, which cancels the remaining reservation.
the other option are some of the county parks, which very often have sites available and some are first come first serve. Many don't use reserve america, but a local number so they often aren't known about except for us locals.
