I notice you have had the mower run for everything from 45 minutes down to 5 minutes, with the time probably getting shorter as you continued to use the mower. It sounds as if the crud you had in the fuel tap was a floating mass rather than a genuine build-up of hard stuff stuck to the interior.
When you get a time-delay feature in a situation of engine cut-out, chances are it is either temperature sensitive (which will have some cause like ignition module failure, cooling system malfunction, exhaust blockage, or lack of exhaust tappet clearance) or time sensitive, in which case it will probably be a fuel system blockage. Because your engine was initially taking so long to cut out, I started off focusing on temperature sensitivity, but once we'd eliminated that, we were left with fuel system. If you had been getting short run-times earlier in the process, it would have made sense to do the time-to-fill-a-cup-with-fuel test sooner. Floating masses in the fuel system are tricky like that though: sometimes no problem at all, sometimes a severe blockage. In this case, the floating mass suddenly blocked the fuel tap almost completely, right after the first time you did the time-to-fill-the-cup test. That sustained rapid fuel flow during the test was all it took to solidify the floating mass into a more compact, more effective blockage.
You need to flush out the tank and its fittings thoroughly now you know there has been floating crud coming out of it.
