I was going to suggest maybe putting wood or something behind the taps to build them out from the door a bit for more clearance, but your idea seemed easier.
you could link the doors together using a bracket and screws so that both doors always open together.
sounds like a massive pain in the posterior to remove the tap handles just to get a slab of meat out of the freezer...
fasten something like to following to the side edges of the doors, two screws in each door