Adding my two cents.
 I'm not 100% sure the MC shop you took it had vast experience on the LS650 engine.  

The std oil leak that gets oil over the fins is most likely the rubber plug in the head.    It's the oil leak that all the older Savages get.  Suzuki redesigned the plug to help reduce the leak.  Like Oldfeller said,  you can see the underside of the plug in the head cavity above the spot where the exhaust pipe is attached to the engine.  The reason the plug is there is to cover the access hole to one of the nuts holding the head on.    

The fix entails, removing seat & gas tank.  Removing the head cover (note: there are no gaskets on the cover, only sealer).  replacing the plug (remember to clean the opening to remove oil film - alcohol works for this), reapplying sealer, putting the cover on, and tank & seat.  A person that worked on LS650 engines can do it in about 30 mins.   Someone that is not familiar, maybe 2+ hours.

It may be a good idea to check the tightness (torque) of the head bolts while the head cover is off.   That is one of the preventive maint. items.