I am not sure what the final goal of your new design is but its basic premise is interesting. Although the initial reaction would be that it would give a higher compression, I am not sure of the answer either because if you use the same piston stroke for both cylinders (which you should initially do in the following calculations) then when you replace the cylindrical cylinder with your conical one then the bottom of stroke volume and therefore the initial gas fill volume of your design will be less than that of the standard cylindrical one.
The way to determine if there is an advantage to your design is to first calculate the volume of a standard cylindrical form container at both the bottom of the stroke and the top of the stroke (I realize that the distance between the piston top and the container top will be very small at the top but it will not be zero. Next divide the top of stroke volume by the bottom of stroke volume for each container configuration. The result of this calculation is known as the compression ratio. Next repeat this same calculation for your conical design. If the compression ratio for your design is greater than the one for the cylindrical one then your assumption is correct.
Just as a note, one issue you will run into the application of your concept is that, even if the discharge pressure is greater, the actual volume of gas discharged with each stroke will be reduced on your unit and it will have to be run at a higher rpm or for a longer period to deliver the same gas volume as a current conventional unit.
The equation for the volume of your conical shape is: V=.2618h(D^2 + Dd + d^2) where, h = the height, D = the diameter of the larger end, and d = the diameter of the smaller end
Note: D^2 = D squared, etc