I am not sure how the throttle linkages would cause this problem unless they are not operating smoothly.
A malfunctioning Intake Air Bypass system is the first thing that comes to mind. The following are the words describing its operation from the manual.
"
Intake Air Bypass (IAB) Control System
With the IAB control system, a IAB control valve is located between the left and right bank intake manifolds and connected to both intake manifolds. In the middle of the chamber is a intake air bypass control valve. Opening and closing movement of the IAB control valve permits the flow of intake air in the intake manifolds to be altered such that the amount of air entering the combustion chambers is maximized. Specifically, the IAB control valve is used to optimize the resonance-charging effect with low and mid-range engine speeds and to optimize the inertia-charging effect with higher engine speeds. The system thus maximizes low-end and mid-range torque and high-end output.
The IAB control system consists mainly of the intake manifolds, the chamber, the IAB control valve, the ECM that makes control to
open and close the IAB control valve, an IAB control solenoid valve, and a diaphragm.
The system controls the IAB control valve open/closed position with reference to the engine speed only.
Closed ¨ Open: When engine speed increases to 3,950 rpm
Open ¨ Closed: When engine speed decreases to 3,750 rpm"
As you can see,it operates in the rpm range that you listed.
It does not necessarily address your idle issues.
Check the vacuum lines, the vacuum tank connections (at the lower rear part of the engine) and electrical connections.
It may also be worthwhile to clean the throttle body for any debris and carbon buildup.
You could also remove the Idle Air Control and clean the carbon out the passages to the throttle body.
Those are some simple things to try.
Generally, the dealer could take it out and get it to malfunction and record the happenings on the HDS. Then they can go back and study what each sensor is doing, it also will tell them when the idle air bypass operates. This info can be shared with the Honda Tech support if they need some help. Hopefully, this would pick up some anomoly. Without solid info as to what the motor is doing, it can be a long guessing game.
Of course, spark plugs and/or wires could always be the simple answer. One intermittant spark plug can cause bizarre problems.
Mike