Unpredictable throttle sorted.
To recap my issue - 2004 rocket III with TTS supercharger, after a long motorway trip, rolled off throttle on slipway and bike stayed at 2000 RPM. Quickly got worse. Bike had a steady but low tickover at 550 RPM. Anywhere between tickover and 2000rpm, bike would lunge, stall and backfire - very dangerous riding around town - but ran perfectly above 2000rpm.
Interweb research suggested the Primary Throttle Sensor (TPS). It was going to be difficult to set up a new TPS, due to MAP sensor and Idle Stepper Motor being removed during SC fit; therefore you could set the TPS at 0.6v, but the ecu will not be able to adapt, as the rest of the ISCV reset can not be performed. Also the engine warning lamp was permanently on.
After fitting new TPS and setting to 0.6v with TuneECU software, did 12 minute tune and rode to test. Bike was just as bad; lethal to ride slow. After much pulling of hair and trying several other things which did not help, I solved it.
The TPS had been set accurately to 0.6v. I now ignored this and tried twisting the TPS slowly at tickover. This raised the tickover to a sweet 800 rpm. I then gave a twist on throttle and the hesitation seemed to have gone. A quick test ride later and amazingly the bike is as smooth as me grannies gums. Not sure what the voltage is at the TPS . . . but who cares.
My analysis is that the TPS must have long ago been reset , during the SC fit. It had failed after 7500 miles, giving my 'unpredictable throttle response' problem. When I replaced it, I set it at 0.6v - which was wrong.
Anyway, thanks to all who have helped work this out; hope this saves someone a few hours time.