[nbleak21]

all of the symptoms you've described can be caused by your EOC method. Cycling the key on many (though not all) vehicles will cause the fuel pump to automatically prime the system by turning on full blast for 2-3 seconds. if your system is already pressurized, this can cause an overly rich mixture at restart.

excess fuel can cause stumbling in many forms:
carbon rich egr (ie: blockages, unburnt fuel into intake, etc)
fuel on the spark plugs (misfire, incomplete burn, etc)
AFR's richer then even the "optimal power" band of 12.5:1 (fuel pooling, incomplete burn, ignition retardation, etc)

Best bet for EOC kill switch is dependent upon the make, model, and year of the vehicle... options include but are not limited to:
-Fuel injector cut-off
-Crank/cam angle sensor
-distributor/coil
-EFI fuse circuit
-fuel pump (mainly mechanical injection diesels, not gasoline engines, for the very reasons stated above)
-intake block off (again, generally a diesel application, and usually only in the case of emergency!)

as far as your particular application, it may be tough, as these newer engines have a LOT more monitoring perimeters, and can throw codes under many more conditions then older generation vehicles, and depending on whether the code is active/passive, may end up throwing your car into limp mode, and then the FE really sucks! (not to mention, if you know you're running on a passive code, a more detrimental active code may rear its head just by coincidence, and you'd have no idea that's happening, and then you're left walking!)

As far as the tech saying to open it up every now and then, I couldn't agree more! on-ramps to interstates are the perfect opportunity, as entering in the flow of traffic at speed is generally much safer (and more convenient) then entering in at a lower speed.
Benefits:
-Detergents in fuel will help clean intake valves/runners
-higher piston speeds help blow out built up carbon on piston surfaces
-prevents cylinder walls from forming ridges near the head
-helps keep EGR system clean by allowing additional purging
-helps clear blockages from Catalytic Converter, muffler, etc.

I'm not advising that you red-line it at every intersection, but that little fit engine was designed to be let loose every once and a while!