Should a gear shift cable repair cost $350

Well, google is your pal here.

The cable is available for about $50. Check RockAuto on http://www.rockauto.com/catalog/raframecatalog.php?carcode=1353169&parttype=8528&a=FRc1353169k429575.

Assuming that the OEM cable is double the price, it looks like the dealer is charging you 2 hours at $125 / hour to fix this. I couldn’t see this taking more than 2 hours ~ including a coffee break.

Sounds a little pricey to me.