If you are happy with the tune other than this, it sounds like you just have to adjust the fuel at off TPS position. Add 5 to 10% fuel at this reading( off TPS). Now I could be wrong, and I have never worked on mine yet, but I remember Pig ( I think) saying something about this.
loaded two different tune's that i'd recieved (hanso, and Evil Mitch). found out that I hadnt reset the tps or the adaptations. fired it up and it was like a brand new bike... for about a minute. after that 1st minute it settled down into a low idle (not hunting like it usually does though). It never once died on me though. the little tps light did turn green in the software but i still wonder if maybe that's the cause.
one more question. dealer wants $135 for the tps. I doubt triumph makes their own tps so maybe just maybe the tps they use is one that is used on other vehicles aswell...