It does sound an awful lot like air in the fuel. As you work your engine harder, it will draw in more fuel as well as more air if there is a leak. once you throttle back, the pump / injectors will be fed more air and less fuel and it will just die away. That said, it could also be a problem with your injectors but they are starting to seem a lot less likely now. Another possibility is that someone has made a bugger of adjusting your injection pump. If (for whatever reason) they have had the throttle lever removed from the splined throttle shaft and not put it back on correctly, it would give a similar problem to the one you describe because the governor will adjust the fuel down too far to idle. They are very accurately set pieces of equipment! Has anyone touched the maximum fuel screw on the back of your injection pump do you know?
-Tom