If Beechside is full, check out Tillicum Beach CG run by the forest service. Reservations haven't come on line yet (six months out is when they start) so you still have a chance to snag a reservation. Not FHU, but some sites do have electric. Those that front the beach don't have hookups and are kind of parallel parking.
Depending on how far south you want to go, we also liked Sunset Bay SP near Coos Bay.
There are other Siuslaw NFS CG's along the coast, a few with electric hookups. Again, reservations open up six months in advance.
I don't know if you've run across this site, but we use it often to find campgrounds in areas where we want to go:
Campground Map Type in the name of a nearby town and it will zoom into that area.