You contradict yourself. Lowering the cylinder (barrel) does increase the compression ratio, as it reduces the volume at TDC. As you state, the compression ratio is a measurement of the ratio of the total volume of the cylinder, including the head area, at bottom dead center, as compared to the volume of the total area above the piston at top dead center. Lowering the cylinder, using a piston with a dome, using a thinner head gasket on an engine with a removable head, using a head with a smaller combustion chamber, etc. are all methods of increasing the compression ratio on various engines.

AV8TOR