Watch for lean out detonation!
Lack of fuel (and lean out) is potentially a very serious problem under boost (acceleration) conditions. If I were you, I would pull the plugs and look for any signs of detonation right after a hesitation expisode. Any signs of melting or deformed electrodes or little spots on the ceramic insulators within the combustion chamber are what you are looking for (and hopefully do not find). If found, this really needs immediate correction.
It sounds as if this may be a common problem in the Callaways. That is a little scary to me, as lean conditions under boost will cause audible and inaudible detonation. This will break top compression rings, pistons, and rods if it is severe enough.
FWIW, my turbo BMW has two pumps. The primary pump is in the tank; there is a pretty good size booster pumper just after the fuel filter in the back of the car. It never has any hesitation problems under acceleration. Are there two pumps in the Corvette/Callaway setup? FWIW, the injection system for the Corvette is really an adaptation of the same Bosch Motronic injection system that is in my 1984 BMW. I hope they kept the two pump setup...
Is there a good technical description of exactly what Callaway did to turboize these cars?
good luck,
Steve