ChrisR: I did some semi-scientific testing of modifications to my diffuser. I discovered that a ball in a ball pen is a perfect subject to test light diffusion: it is like a 180 degrees fisheye lens showing the whole diffuser; it is small enough (0.5mm) to fit into your FOV even at 20:1; you don't need to stack to see the whole diffuser sharp; and it is already conveniently attached to a holder (the pen).
I measured two numbers for each setup: the exposure loss in the brightest spot (using my original lighting as a point of reference), and the light contrast (brightness in the bottom half divided by the brightness in the top half).
Here is my original lighting setup: flash with a built-in diffuser + a bottom diffuser (a large sheet of paper). The exposure loss is 0EV; the contrast is 0.53 (so bottom is ~2x darker than the top - not great):
Flash diffuser + bottom diffuser by
First Last, on Flickr
Then I removed the bottom diffuser; the exposure was 0EV, the contrast got noticeable worse (0.40) - so inverse square or not, the bottom diffuser is really important:
Flash diffuser by
First Last, on Flickr
Then I did what I hoped would be the only fix I need - I added a small piece of white paper right on top of the cone (a top diffuser), and put back the bottom diffuser. I lost quite a bit of light at the top (-1.5EV), but the contrast became a very reasonable 0.74. Actually my goal is not to get to 100% flat light - I still want some shadows, so placing a small diffuser on the top indeed seems to be the only fix I needed:
Flash diffuser + bottom diffuser + top diffuser by
First Last, on Flickr
Finally, I tried your other suggestion - removed the flash' built-in diffuser (the bottom and top diffusers stayed). I gained some light at the top (now the loss is only -0.75EV), but at the expense of worse contrast (down to 0.69):
Bottom diffuser + top diffuser by
First Last, on Flickr
So I think I converged to a good compromise - a combination of flash diffuser, large bottom diffuser, and a small paper diffuser placed on the top of the cone results in nice diffuse light, and hopefully sufficient illumination at 1/16 flash power and ISO 200 (to be tested).