Re-reading your post kinda points to a fuel problem, doesn't it? Like the fuel pressure is faling. If you have 2 gas tanks, does switching tanks make a difference? If it does, I would suspect the sending unit in the "bad tank". If there's no difference, don't despair-there's still all kinds of stuff to check-

the air filter and/or the fuel filter, the egr valve, actually, hooking it up to an analyzer might throw a code and give you a fix.