prolonged cranking before the engine starts in the morning

Its hard to guess without seeing the car first hand. I am wondering if the car is loosing fuel pressure or is slow to build up fuel pressure in the fuel injector rail in the morning. This would need to be verified by attaching a fuel pressure gauge in the fuel rail. Your engine has 4 separate ignition coils, if one was failing you may experience a misfire under load or rough running. Has your Check Engine Light come on? Even if it hasn't there may be information in computer of your car that may help diagnose the problem. Your car does have a fuel pump relay but these in my experience do not give the problem that earlier Honda's did. You don't say how many miles are on your car. Perhaps replacing the spark plugs and adjusting the valves may be called for.