Check out Feltz Sawmill in Raeford, NC or MAC's Slabs in Raeford, NC. There is also Ballash Woodworks in Fayetteville, NC who may have some lumber to fit your needs.
Not sure how much of a drive that would be for you but it would be shorter than a trip to Raleigh. I believe MAC's does do some delivery work but don't know his radius of travel.
Oak is something I am fairly certain they will have because it is so common around here, not sure about cypress.