Yes, fuel flows freely out of the filter ...Fuel filter and tank tap both working OK?
Yes, that could be a good idea, except it seems like it only uses the fuel already in the bowls. I accidentally ran it until it stopped and then noticed that I hadn't even turned on the fuel tap.It still sounds like a fuel problem. How long does it take to start to run rough and then cut out? Perhaps worth trying to simulate it running out of fuel so you control this to see if the symptoms are the same? If it takes 10 minutes for example, you could starve it of fuel after say 5 minutes and see what happens. If it runs rough and cuts out in the same way then it looks like fuel but if its different then perhaps something else.
I could try emptying both bowls, and then see how the flow through the drain tube looks after they empty ... if it flows uninterrupted, I'll know if it's fuel or electricity related