A blown turbo can't cause an engine to shutdown. Ok at idle you say, runs rough when you apply power, leading to a motor stall? Presumably box in neutral?.
Odd on its fuel related, either you not getting enough air in, or fuel in. Is it the same hot or cold?
The last time I encountered this problem, in was fuel filter relaleted, and that was less than three hours running afterwards. We had a mixture of the bug, and condensate in the tank. This got churned up whilst motorsailing with an angle of lean on.