Went through the exact same issues with my 06 speed triple for the last two years. I boiled it down to the ICSV Stepper Motor or the TPS, aka Throttle Position Sensor. Got tired of taking the tank off and putting it back on so I trailered the bitch to a reputable Triumph dealer one hour away. Ended up being the TPS. $200 dollar fix and was worth every penny after my countless failures in diagnosis and solutions.
It could be your tune, but I highly doubt that. My money is on TPS over stepper motor or tune. But it could be any three of those.
Sent from my iPhone using Tapatalk