Old or new, a properly tuned and configured Honda engine should not surge. From idle~WOT (wide-open-throttle), it should be smooth and steady, with no real noticeable change in engine RPMs
Ideally, you'd want to totally drain all the old fuel, flush the tank and lines with fuel system cleaner or solvent and add fresh, regular unleaded gasoline.
Next best option is to pour in some fuel system cleaner to the tank (such as SeaFoam or the like) and it might just do the trick.
In the future, try to purchase regular unleaded with either ZERO ethanol or as low to zero ethanol as possible. You just need regular 86 octane. No benefit to using higher octane fuel unless it offers lower ethanol percentage.
Add some fuel stabilizer to your fuel can to greatly extend the life of the stored fuel.