That is all clear, Peter, but what is wrong is less so. First, if you run it without the filter and cover, does the spark plug stay healthy (dry, and more grey than black)? If so, the small intake restriction from the filter and housing may be affecting the carburetion, perhaps by blocking the air bleed. However I proposed a similar analysis in Paul's chonda thread when he reported the same symptom - the problem was that the presence or absence of the air filter actually had nothing to do with the symptom in that case, the real problem was that the ride-on mower was applying voltage to his kill wire and causing an ignition malfunction, all else was coincidence.
So, I'm proposing that you do a couple of with-and-without tests to get the situation clear at the beginning. I'd like to eliminate any possibility of coincidence causing symptoms, rather than whatever change you were attempting to test.