Good thinking: secure fuel lines are kind of fundamental. The only advantages of those spring clamps that I have noticed, are first that they are much easier to assemble in the factory, and second, are less likely to be overtightened or undertightened by insufficiently skilled repairers. I get a bit annoyed with the spring ones twisting out of the pliers at the crucial moment, but once they are on they are one less thing to worry about, which I wouldn't really say about the screw-clamp ones because of possible improper tightening at some point in time. Sounds like your hose is either incorrectly routed or too short. I bet it was long enough when the mower was new, so if it is wrong, either it has been shortened or somebody has messed up the routing. Don't get inventive with fuel hose routing: putting the hose too close to something hot is both dangerous, and prone to causing vapour lock, so following the original design is best.
You could do your ten minute flooding test while you are waiting for your new fuel line to arrive. Once you have done that successfully, you know that the original problem is fixed: when you started, fuel was coming out of the carburetor. Don't be too surprised if some fuel came out of the main jet during your swishing and tilting test: there is nothing to prevent it, if the fuel level momentarily rises above normal due to tsunami effects inside the float bowl.
