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The rate at which a turbo makes boost is a function of the wastegate combined with the the actual sizing of the turbo. A different tune won't help you build boost faster on this kind of setup. If the computer controlles the wastegate (like on an STI or Evo) then a tune may help some. The only tune issue it could be is if the tune has you ridiculously rich.
How are your O2 sensors? a bad O2 sensor would have the car dumping fuel into the chamber, which would result in lower exhaust temps, which would mean poor turbo response. Your also 100% sure your piping couplers are all tight, and no intake or intercooler leaks?