Dirty fuel filter would be the most obvious problem. Either that or the pump, but most likely, it's just a clogged/dirty filter. You will get the exact symptoms you describe, because there's enough fuel for normal running, but when you need power for accelerating or any other load, you choke the engine.

Also just noticed that you use the fuel system cleaner, now I'm absolutely sure this is your problem! When you use that, it breaks up all the gum and gunk in the tank and sends it thru the lines, where the filter gets overloaded with it and clogs much quicker.

Easy thing to try and eliminate if nothing else! Let us know.