I had the convection option in my last stove--a dual fuel Jenn Air. Loved loved loved the gas burners because of the instant on/off heat. I also used the convection once and could not figure out why people raved about it.
And then we moved. I now have an electric glass top GE and hate the thing with a passion. I could not figure out why my canning was so hit and miss last summer--until I realized that the burners kept cycling on and off as they reached the temperature required. You could actually see the 'red' of the burner coming on and then fading out and then coming back on. So there is never a constant heat for cooking. My neighbour who has the same stove, did not believe me until I showed her using a pot with a couple of inches of water in it. The water came to a boil and, with a gas stove or even a coil electric stove, would remain at that boil or even boil more vigourously until the heat setting is changed. With mine, the boil lessened and then became more vigourous as the burner cycled. I guess it has some sort of thermostat that turns the heat on and off like a furnace.
I have been searching for a gas or dual fuel to replace it and am very frustrated but for a different reason. The current trend to have an extra middle burner, has moved the placement of the other burners closer to the sides of the stove. But if you are using a canner or large stock pot, the edge of your pot is now very close to your counter top and could easily cause heat damage. Grrrrrrr!!!
Okay rant over. Chasing Hawk I wish you the best of luck in your search. And let us know if you get a stove with the convection oven option and how often you use it.