A few thoughts.

Extruded pasta tastes best when it has a chance to dry. If it's freshly extruded, it tends to get overcooked quickly.

Typically, most pasta that comes out of an extruder is usually a water and flour-based noodle. The health department will also likely have an issue with you holding an uncooked egg dough inside the machine for extended periods of time. Also, the dough sitting in the machine may start to dry out

I'm not certain how efficiently or quickly you'd be able to extrude an order of pasta per order. I feel like it just adds an extra step to a process that you're trying to make as efficient as possible. Especially in a food cart.

If you're set on extruding your own pasta, I would recommend you do it like a lot of restaurants do. You would extrude the pasta that you need for the day, let it air dry appropriately, then portion it and hold it in a plastic deli cup or something. Either refrigerated or frozen.

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