Is it possible to remove/replace the fresh air/defroster controller without first removing the cables from the distribution valves and blower? And if the answer is no, then does that mean that I must remove the gas tank to gain access to the bottom of the blower to remove the cable?

You can pull the control away from the dash if you remove the 6mm bolt under, on the back side. You cannot completely remove without disconnecting the cables from the front trunk. I have heard of removal of the fresh are box without removing the gas tank but this would be the hard way to do it.