Here's a possiblity:
sounds like it's got enough fuel to idle, but not enough to cope under load. Is it possible that the problem lies with:
: fuel pressure regulator
: fuel pump
: fuel lines
did this problem suddenly begin all at once? What you described, is exactly what happens when you starve an engine of fuel. Long shot, but your pump may be putting out insufficient pressure, or a fuel line may be pinched. I'm thinking pump is far more likely though