I don't understand why you're saying a funnel doesn't change the surface area. It seems to me it obviously would. Is there something I'm missing here?
Little opening = small surface area of trapped air to water
Bigger opening = larger surface area of trapped air to water
Right? Assuming the funnel shape doesn't increase the volume of the trapped air too much that it offsets the gain.
Unless this is exactly what you mean, that the funnel increases the ratio of air volume to surface area too much. Which I'm definitely too lazy to try and calculate to see.