Can't speak for anyone else, but my Automatic Laser Musket is moddable on the workbench until I equip it. Then it disappears from the workbench list until I drop it and pick it up.
The Automatic Laser Musket has a decent fire rate since it loads 20 ammo at once and each crank fires one shot. It is much faster than the standard Laser Musket since you crank it 1 to 6 times for each shot.
Unlike every other Legendary weapon, it has a unique mod instead of a Legendary bonus. So it is impossible to get an Automatic Six-Crank Laser Musket. Choosing a different crank other than automatic converts the weapon back to a regular Laser Musket and removes the Automatic mod from your inventory.
Haven't seen any other type of Legendary Laser Musket. You can use console commands to add a different Legendary effect to a Laser Musket, but that is only available for PCs at the moment. Tried one crank on a Two Shot Laser Musket and it did twice the damage. Also, Two Shot weapons actually only use up one ammo instead of 2. So a Two Shot Six-Crank Laser Musket would use up 6 Fusion Cells at once instead of 12, but give the same effect as using 12 cells on a regular Six-Crank Laser Musket. Which is why a Big Boy with the MIRV Launcher is so fun.