That scratch is not likely to cause a problem.  I have had deeper scratchs and the engine ran fine.  As estradajae said if the engine has compression it is fine.  Besides your engine doesn't sound like an engine with poor compression.  That would be hard to start hot, poor idle (not just after a flight), and low power.  However, if the scratch is recent it could be causing the piston to jam a bit, extra run time may get rid of that problem.  IMO it is something causing your restarts to be too rich.