If it works properly with a different carburetor, your fault is in the original carburetor. Since you are sure the float bowl is filling, it can only be the main jet or one of the associated drillings. I think you need a manual that shows how the carburetor works and how to service it. Best guess is you haven't found the main jet yet, and it is still blocked. Second best guess is there is a lump of crud in one of the drilled holes and you haven't blown that one out yet. This is all based on your statements that the float bowl is filling properly, and the mower runs properly when you replace the carburetor.
