This is a long shot but I have seen similar problems caused by debris in the fuel tank. Under load and increased fuel flow demand, the debris would restrict the fuel pickup in the tank. When allowed to sit, the debris would settle away from the fuel pickup and allow normal flow until it plugged up again.
'07 Winnebago Journey 34H, ISB-02, MH2500
Toad - '08 Ford Taurus X
Blue Ox, Aventa
US Gear UBS