Smoke is a very good indicator of what's going on. Black smoke is too much fuel, not enough air, or too much load. White smoke is generally not enough compression to ignite the fuel charge.
You're saying you have black smoke as it bogs and dies, this is not starving for fuel, if it's starving for fuel, you wouldn't get smoke, as there is no fuel being burnt to smoke.
It almost sounds like your engine is being loaded down, causing this issue. Could you have issues with the pump somehow?
We had an engine in the workshop that had a similar issue, it would run, then bog down, smoke and stop, let it cool and it would do the same thing. Turned out to be the main bearings, it would run fine till it got warm, then the bearings would grab, then load the engine down. The symptoms made sense, but it still had good oil pressure.