Pictures of the desk?
I would take the cabinet I like best and make whatever changes are necessary to fit the Necchi. If someone cut down the lip you can always glue another piece of wood in to build it back up. OTOH I never have enough storage next to my machine. The desk (ugly or not) might be just the thing.
I tend to get rid of cheaply made ugly cabinets. Think particle board from the 70s with printed "wood". I strip everything usable and trash the rest. I don't have room to store bad ones. An older cabinet made with quality materials is worth saving though.
Your broken cases are still good for storing machines. They will at least keep dust and dirt off them. You may be able to fix them too if the hinges are still there. The empty case is probably intended for a free arm machine.
Rodney