It does sound like there are obstructions in either the drilled holes in the carburetor body, or the jets. The most likely source of your problem is dirt in the passages in the fuel bowl nut, which are notoriously troublesome with that carburetor. If you didn't use a good blast of carb cleaner through there, and probe the passage after blowing out the cleaner with compressed air, it may still be obstructed. I suggest that you run carefully through this cleaning procedure:
http://outdoorpowerinfo.com/repairs/briggs_walbro_lms_carb.asp
