Well i dont know much on the specs but in theory, the fuel pressure should not be dropping with more throttle. I would go the the dealer and tell them to look at the fuel pump.
Ummm i dont know if this will be the same but my dads 2008 Tahoe was doing something similar, It would start very hard, he would be driving along and the light would come on then go off many times over and over, found out that it was a fuel pump. I would have your dealer check your fuel pump pressure. May or may not be the same thing but it sounds very similar