adjustable gate....Hmm! forgot about that..... firmly sealed with the engine off and spring pressure holding it firmly closed ??
Slow boost build-up could be through a small amount of wastegate creep (i.e enough to relieve a small of exhaust pressure).
give it one turn tighter and drive it again (sanely) and see if it improves or not.
You'll be trying to find the happy medium between w/g creep (too loose) and boost spike (too tight).
I did a T04E onto a 13b turbo in an early Rx-7 ages ago...took me a couple of hours of trial and error to get the actuator rod to the best length / best w/g preload.
The old Rs' Lib would blink the CEL on overboost (16.5 psi) if you hit over that twice the third time you'd hit the wall (boost cut), the CEL would stay lit and lower the boost cut to 7 psi until the engine was shut off and restarted.........no fun on a cold winters night
