I have now had a chance to make a prototype and test the result. I used a reversed design that I had tried much earlier in the efforts to fine a good reliable reed design but this time I used a solid machined version based on the design by Richard Evans. The results showed that although a small difference was measurable the effect of reducing the internal volume was minimal. reducing the volume by 6mm (changing the 6mm long screw for a 12mm long screw) raised the pitch by 20 cents which was the same as moving the sliding part 2.5mm.:-

