Well I've been trying today to spawn a CP ship. The S40K Phoenix Hawk-Class Light Pinnace to be exact.
I have exactly 21,900 CPs, yet every time I try to exchange them for the ship I get the message: "You are trying to exchange for more CPs than you actually own." And it's not only this particular ship, but it's the same story with the C-Wing Ugly. Also, I'm in a Starport, so there shouldn't be a problem with location.