I agree with others that you want to bore/grind out the pith and see what volume you have in the measure. Then, if after getting rid of the pith you find you don't have enough volume, you drill/bore more into the solid material.
I don't know about others, but I don't want "open pith" inside my measure as powder will stick and not give a uniform charge. Now the pith can be sealed off using crazy glue or Minwax's wood sealer, but that sort of defeats the attempt at authenticity of using the antler measure. Such problems then probably were the reason that tinned iron measures were so popular back then.
Gus