For the OP (Sadie):

Two miles on unsafe calipers is two too many, if the brakes don't work. 600 miles on a system that may need some maintenance but is otherwise safe might be okay as long as you're aware of the issues. If the mechanic didn't say "these are unsafe and I recommend you leave the car here" then you may be okay going to SC.

Are there symptoms, or just a "your calipers are bad" recommendation from a new mechanic?

Do you have to pump the brakes to stop? Does the pedal sink? Do the brakes feel mushy? Do they squeal? Is there brake fluid on the ground or on the calipers? Are the pads wet with fluid? Did you rear-end someone and discover they didn't work? (kidding)

Diagnosing a need for new calipers without knowing the symptoms is tough. Normal reasons would be obvious leaks, excessive uneven pad wear that indicates a stuck caliper (compare inside/outside), stuff like that. Other symptoms like mushy pedal might mean old fluid with moisture or air in the lines; things like hard to brake or dragging and overheating brakes might be a master cylinder.