I had a similar hesitation under part throttle, almost like the car was running out of fuel! And yet it worked great at w.o.t! Also a back fire out of both side pipes while down shifting or easing off the accelerator.
I noticed a spary pattern of dry fuel on the passenger side valve cover and on the fuel log, It turned out that the six phillip head screws that hold the base plate to the main body of the demon carb had loosened and caused a small vacum leak between that gasket. I hope yours is an easy fix!
