To test you can leave the filter off... I suppose. We all know it's not good but till we get it running better, it'll do.
This could be a fuel supply issue.
FYI: petcock on prime will flow fuel constantly. In the on position, it takes vaccum from the motor to open the diaphram and let fuel flow.
Looking at the carb on the right side of the motor:: the front hole on the carb is a vent. The middle is the fuel supply. The back hole is the vaccum.
Let us know how you make out.