Barn The Spoon posted up a short video on his blog in which he carves one of his octagonal handled eating spoons. Watching him carve, everything clicked (or at least in relation to this particular issue).
In order to achieve the scooped top to the bowl, Barn creates a convex top first, then when everything in the middle is carved away, only the perimeter of the bowl defines the topography. It's much easier to see in the video than try to understand by writing. The reason I couldn't work out how to create this effect is that I was thinking too much in two dimensions; top view and side view. To create this effect, it must be approached in three dimensions. Once it's clear in the mind, it's very easy to achieve.
An interesting side effect of creating this scoop top to the bowl is that hollowing the bowl seems much easier. I am having fewer issues with fibers tearing and running out, and overall am getting a pretty smooth finish in there.
The two spoons shown here (and I also carved a third) are fairly crude overall, but my main focus was on that one aspect of the bowl, which with a little refining will be exactly what I have been seeking. In short, this is a public thanks to Barn The Spoon for helping out fellow spooners around the world refine their craft, and for acting as inspiration to anyone that thinks they can't be successful in pursuing their dream.