The driven clutch is normally closed. The drive clutch is normally open. As the RPMs of the
Engine increase the drive begins to close and applies pressure to the belt, transferring power to the belt causing the driven to spin and open with rotation.
You mentioned that you only have the high idle when you are moving. This could indicate that one of the clutches is not returning to its normal state (driven closed and drive clutch open) to allow the belt to no longer be engaged. Thus transferring the power of rolling from the tires to the driveline and rotating the Engine giving a higher than normal idle. You said if it is in neutral the idle returns normally.
Think of it as downshifting a manual clutch driveline, using the lower gears as a Engine break. The RPMs or idle of the Engine increase as you roll, until you come to a stop.
As you know the variable speed clutches do all the shift for you, so you are always in the right gear. Power when you need it and speed when you need it. That is when the clutches are performing properly.
If it was me I would remove the belt covers and observe the clutches in action. Placing a black line on the clutch face will also tell you if the clutch is opening and closing properly as the mark will wear off. If only part of the line is wore off then this would indicate the clutch is not allowing full travel of the belt across the face of the clutch.
Again just my thoughts.