2009 Hyundai Sonata surges at takeoff and acceleration

I have a 2009 Hyundai Sonata which has been a great car, having had only one problem with the starter in the seven years that I've owned it. But now, there seems to be a 'lag' in the throttle in takeoff from a stop or when decelerating then reaccelerating.

At a stop, if I press on the pedal slowly, there is no response until I continue to press on it slightly father. When it finally starts to accelerate, it does so with a sudden jerk or surge. What would cause this? I thought maybe the throttle cable, but more knowledgeable people than I told me that it has an electronic throttle body and no accelerator 'cable' per se.

Someone suggested the possibility of carbon deposits on the throttle plate, but I removed the air cleaner cover and boot and from what I can see inside the throttle body, there does not appear to be any deposits on the throttle plate. A little discoloration around the top and bottom edges of the plate, but nothing that I would call carbon deposits.

I've been told not to try to open the throttle plate by hand... To turn the car's ignition to the run position and have someone depress the gas pedal until the throttle plate opens. I tried this, but the plate does not move unless I actually start the car.

I'm not even sure this is the problem. I really don't see anything that I would consider a build-up on the throttle plate. It's a difficult place to see and even harder to reach in to. Does anyone have any suggestions as to how I might clean the throttle plate, or if there is another unrelated problem that might be causing the car to surge on takeoff.  It's getting worse and I'm afraid I am going to rear-end the car in front of me at a stop if I don't get it fixed soon.