Neutrally bouyant. Sounds like a good idea, but it's much more complex than you would think. I've been working on this problem for years; I'm sure Todd has also. He has almost achieved this with his ToBo Crawdad (see this fly on the flytyingforum.com). With the ToBo Crawdad, Todd has come up with an almost-neutral fly that imitates the ACTION of a fleeing crawdad very closely. However, doing this with a fly that has a "lip" or "face" that causes the wiggle, is a complex problem. You see, there is a fine balance between gravity pulling the fly down, and Archimedes principle pushing the fly back up. Without this "floating" quality, the fly would be more likely to roll, and then you end up with a fly similar to several other designs out there that "wiggle", except they wiggle a short ways and then they roll, and twist your line. So Todd's Wiggle Minnow is really a triumph in Design, in that it is the first fly to have a "resonance" or "wiggle" like that of an engineered plug without rolling.
Using heavier foam, or a heavier hook, or adding weight to the inside, all have a similar effect: they make the overall density of the fly higher, but the inevitable effect of this density, is that it reduces the "wiggle" or "resonance" of the fly. The more weight you add, the less the fly wiggles, and the more it is just dead in the water; that is, it no longer wiggles effectively. This has been done before, and it is called a Gummy Minnow (hehe)--neat looking fly, but zero-action. I've tried all varieties, and my conclusion is that, even with just a little density or weight added to this design, the benefit gained does not outweigh (pun intended) the disadvantage of the loss of "wiggle".
So how do engineered plugs wiggle without rolling? That is a good question....but the answer is beyond the scope of this...
I think the "answer" to this fly-design question, is to adjust your sink-tip. Using a flourocarbon leader of 10-50 inches and 8 to 20-pound test, I have been able to fish Todd's Wiggle Minnow effectively in shallow or deep water. In very shallow water, for river smallies or largemouth in a shallow pond, for example, I use a longer leader (about 4 feet) and floating or clear-intermediate line. In deeper, faster water, I use a 400-grain sink-tip and a 10-inch leader. Another thing I like to do to all of my dark-colored sink-tips is to color the entire tip with black permanent marker; this tends to erase any shine that might be on the tip or loop-to-loop connection.
That is my $.02 on Todd's Wiggle Minnow; hope this helps.