Hot water dispenser - how to replace supply line.

Have a Anaheim Manf Co. Quick n' Hot dispenser with a dual faucet dispenser. The 3/8" supply line the plumber installed deteriorated and is now leaking after a few years of use. I can't figure out how to disconnect the supply line from the faucet side. I have loosened the locking nut under the faucet although was not able to pull out the faucet because the copper lines are spread apart and cause an obstruction. Access to the faucet is very limited, basically have a square peg round hole situation. Is there anyway to pull up the faucet dispenser without bending the copper lines. Do I need to cut the copper lines to pull out the faucet and start fresh? Is there a plumber's secret to share on how to get the dispenser out with out creating a larger project.