Kevin:
I've explored vibration issues in the past with my 912 UL. In my engine installation there are two rpm bands where vibration is noticeable - 3,800 to 4,100 rpm and 4,300 to 4,800 rpm.
I guess I'll start by saying there's a known vibration problem with the 912 ULS. Rotax Service Letter SL-912-010 (attached) identifies the problem as resonance in the 3,600 to 4,800 rpm range. There are a number of contributing factors listed in SL-912-010, but Rotax does not identify a definitive root cause. Rotax does say the problem is often reduced by the installation of a slipper clutch.
Now here's what I've found. First, it's important to understand the nature of the problem. The 912-series engines are very well-balanced except for one vibration mode that's intrinsic to four cylinder boxer engines. The layout of the cylinders means that the engine produces "rocking couple" vibration that twists the engine around a vertical axis and tends to wag the prop from side to side. This vibration mode is not well understood in the Rotax community, imho. It means, for example, that the flat bed-type engine mounts found in many aircraft are not a good idea as the flat bed configuration is poor at damping rocking couple vibration. In my aircraft, which has a bed mount, there are witness marks around the Lord mounts that show the Lord mounts are moving from side to side. A dynafocal type mount is a better engine mount for the 912 as it's much better at damping rocking couple vibration.
As part of my vibration exploration on my 912 UL I installed a 912 ULS gearbox (without slipper clutch) which has a 2.43:1 reduction ratio in place of the standard 912 UL gearbox which has a 2.273:1 reduction ratio. I found the vibration was worse with the 912 ULS gearbox with all other factors the same (I did repitch the prop). I also took noise measurements with a dB meter and got a very interesting result with the 912 ULS gearbox. There was a noise peak at 4,500 rpm that was not present with the 912 UL gearbox. I interpreted that as mechanical resonance.
This result - more vibration with the 912 ULS gearbox - together with Rotax's suggestion in SL-912-010 to install a slipper clutch, leads me to the conclusion that vibration issues on 912 series engines are the result of an interaction between aerodynamic propeller loads and the inherent 912 rocking couple vibration.
So, what to do about it? In principle the answer is a well-designed dynafocal engine mount to adequately damp rocking couple vibration and a slipper clutch to break the direct mechanical connection between propeller and crankshaft.
On your aircraft, I'd start with prop pitch. There's something about the aerodynamic load on the prop blades that's exciting resonant vibration when you throttle back. We don't really know what it is so you'll have to experiment. An overpitched prop exerts more driving force on the gearbox when throttle is reduced. Your prop is overpitched, so the first thing I'd do is reduce the blade pitch to increase your static rpm above 5,000. At the same time I'd ensure that the pitch of all three blades is identical.
Then I'd suggest you inspect your engine mount very carefully. Look closely at each mount point for any damage or cracking. Look for capture washers contacting the mount where they shouldn't be. Make sure the engine mount's in factory condition. The rubber shock mounts are (may be) available in different hardnesses with different damping characteristics. Experiment with different shock mounts.
If all else fails, install a slipper clutch. This is not often done on 912 UL gearboxes as there's something about the 912 UL gearbox reduction ratio that makes the 912 UL less prone to the vibration problem. But it would undoubtedly help on the 912 UL just as it does on the 912 ULS.
Mike Brown
SL-912-010AbnormalVibration.pdf (You do not have access to download this file.)