Not sure what 'damper' is being referred to here but, yeah, the
pressure plate springs might very well be tired and the clutch needs to be replaced.
Could also be a stretched clutch cable but that would probably be too easy.
A new King Cobra clutch costs about $200., plus a new release bearing ($30.) as well as a new pilot bearing ($15.) Turning down the flywheel is under $50.
There is no need to pull the engine to replace the clutch on a Mustang. You have to pull the tranny of course and this is also a good time to replace the rear main seal on the engine (under $20.).
Labor for a clutch replacement shouldn't run much over three hours, tops, for an experienced mechanic with a lift and proper tools. Probably less time, in reality.
You
could spend $600. but that sounds a bit high, even at inflated labor rates.