First, welcome to the site. I hope you have many miles of wide grins with your trike.
Anytime that I hear of throttle "sticking" issues on a 2006 or earlier, my first thoughts are of the primary throttle position sensor. The TPS is one of the most common issues with the early models. The symptoms are close to what your describe. Revs apparently stick around 2,000-2,500 rpm but return to normal after a shutdown and restart.
The early TPSs have a black interior (unfortunately you have to remove it to see). Being basically a rheostat, they typically develop a flat spot at the angle that corresponds with normal cruising rpm's. This can occur as early as 8,000 miles but most start to show up around 15,000 miles.
The new part number TPS has a blue interior.
If you have some mechanical eptitude, it's not a difficult replacement but you do need to calibrate the installation. This is where the Tuneboy ($$) or TuneECU (free) products come in to play. Otherwise, you will most like need a trip to the dealer.