Uhaul trailer to allow sheets of 4x8 lie flat (either open or enclosed) is only $18.95 per day. Cheaper than the MDF, and less chance for damage than a roof rack.
Can you store core on its long edge if it has a perpendicular base (sort of like an 'L' built on a 5degree angle)? Or does it have to store flat? Do you cut it with a hot wire, a knife, or a saw?