My 1978 280Z has severe rust on rockers and underneath. No rust in trunk or engine compartment. Car runs great.

Can/Should it be fixed or do I part it out?

One man's "severe" is another man's "no problem".  "Underneath" covers a lot of area.  "Should" is subjective.

Not enough here to give an opinion.  Do you have a camera?

Pictures would help: Along the rockers, under the battery, the frame in the front wheel wells, down low behind the doors. Start with that...