Stumble stumble...
I hate to say it, but if it hasn't been done before, the filter sock on the fuel sending unit's pick-up tube might need to be changed. They are the first line of defense in the fuel system.
Before pulling the sending unit unnecessarily, you could run a length of fuel line to the pump from a gas can and see if you get the same stumble. If you do, then it probably isn't a clogged sock. If you don't get the stumble, you might want to check the sock for crud.
Jerry