The resolution of the display would be 640 x 1040 pixels (iPhone 4S: 640x960 pixels). The 80 extra pixels on the vertical axis will allow for more content on screen -- but it's probably not quite enough for another row of icons. I chose this resolution as it seemed to fit nicely in the available space.
That's a good effort, but I really think you could fit a lot more screen in the space.
Let's start with 326 PPI. Per Apple, that's the pixel density of the retina display used by today's iPhone 4S. Now, knowing that the screen size today is 960x640 (I like to list the largest dimension first), we can calculate the exact size of the screen:
W: 960/326 = 2.94"
H: 640/326 = 1.96"
Now, let's consider the overall size of the iPhone 4S (again, per Apple):
W: 4.50"
H: 2.31"
So, as you've already noticed, we obviously have some additional space to work with on the front of the device above and beyond what the current screen requires. Here we can see exactly how much - over 1.5" on the larger dimension nearly 0.5" inch on the smaller one.
Since it is a fairly standard (and useful) resolution, for the sake of argument, let's see how big a 1280x720 display at 326 PPI would be, and whether it would fit the current form factor:
W: 1280/326 = 3.93"
H: 720/326 = 2.21"
Well whaddya know? It fits. Ah, but there are now some issues we've created here:
a) What about the home button and the speaker? There's just over a half inch of space left to accomodate both of them.
b) What about the bezel-size on the small dimension? Current technology may not allow for just 0.05" worth of bezel.
c) What about all the apps already designed for 964x640?
For issue (a), there are a couple solutions. We could move the speaker out more toward the edge of the phone. Additionally, we can either move the home button out toward the edge as well and make it smaller. Or, just remove it altogether, similar to the Nokia N9. Note that in the latter case we could even reposition the screen so it is not centered across the longer dimension of the phone. This would potentially allow us to leave the speaker right where it is today.
For issue (b), the only solution would be to increase the size just a bit. But the good news is it would only be slightly and few would even notice the size increase.
For (c), like I said in an earlier post, you can just use a 960x640 region of the new screen. The nice thing is that since we've kept pixel density the same, the apps will look and behave exactly like they do today.
That's my thoughts. In any case, one thing seems abundantly clear to me: as the iPhone evolves, the screen will take up more and more of the phone's face. I suppose the other side of the argument would be to advocate keeping the screen where it is and shrinking the phone. And maybe there is a demand for such a device as well. But I'd suggest that since we are all used to the current size already, it makes more sense to optimize the use of that space rather than shrinking it down.