The Japanese did experimental work with developing a Gerlich type taperbore round for a 13mm machinegun during WWII. They developed a muzzle velocity of 1300 m/s but the resulting bore pressure was too high. To reduce pressure they mixed small grain propellant with larger chopped cord propellant, which was partially successful. A typical projectile had two copper skirts on a steel body. One design used a one-piece copper projectile (possibly gilding metal, but there was no mention of that). Tests showed this design did not fit tightly in the barrel when fired. At least three different barel designs were also tried. Design and testing was far from complete when the war ended, which stopped all further development.
Sorry for the quality of the drawing, but my original is not much better.
Sorry for the quality of the drawing, but my original is not much better.