When you are doing the swishing-and-tilting test (technical term) you should put your finger over the fuel hose connection on the carburetor. Don't tilt it beyond a normal tilt-angle for safe operation of the mower. In that test you are only looking for wetness on the outside of the float bowl, due to fuel passing between the carburetor body and the top of the float bowl.
When you do the static fuel pressure test (fuel hose connected, fuel on, carburetor level, watch for ten minutes) there should not be any fuel comes out of anything. The float bowl should fill, the float should shut off the needle-and-seat, and then nothing should happen except the grass keeps growing.
Now that you have found the model numbers and codes, you should follow Bruce's advice from early in this process and check in the parts and manuals section of this site. There may be an owner manual there - I don't know. Because your engine has a manual choke (mine is automatic - <<smug mode on>>) you can easily prevent it from starting, or running decently, just by not choking it when you should, or choking it when you shouldn't. As Joe said at the beginning, you might even get it to leak petrol from the breather tube if you over-choked it then stopped it.
