My first thought is that the best way to get rid of all the dead volume, is of course to fill it with something. But... that's not so easy. What about hydraulic fluid of some sort?
Well if you just put some sort of liquid into a normal pump, the liquid will just be ejected past the check valve, but such a problem can be easily fixed by just flipping the whole pump upside-down. Now, you have no dead volume. For one pump stroke.
So, place a very weak spring on what was previously the pump head to hold it in the "pump" position, and force it to generate a slight vacuum before sliding into the "fill" position, and preventing any backflow of the hydraulic fluid out of the compressed volume.
Will this work? In theory? It seems pretty workable to me... but something tells me that with something this simple... somebody has already done it. I might try implementing this on my pump (as it's not quite finished yet and has room for additions). Suggestions and comments are very much welcome.
Oh, and I bet there's a patent on this already.
EDIT: Diagram:

Brass colour is the pump structure, black is sealing material, red is a spring, blue is dead volume, to be filled by a liquid of some sort, and the grey is the pump head.